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学者姓名：彭良雪
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摘要 ：
In this article, we introduce two notions which are called property (sigma-A) and property (sigma-B). They are generalizations of property (A) and property (B), respectively. Every space with a point-countable base (or sigma-NSR pair-base) satisfies property (sigma-A). Every space with the Collins-Roscoe property satisfies property (sigma-B). We show that every compact Hausdorff space with property (sigma-A) is metrizable. Thus some known conclusions can be generalized. This shows that property (sigma-A) plays a key role in the metrizability of compact Hausdorff spaces. We show that the properties of property (sigma-A) and property (sigma-B) are closed under finite products. Every finite product of T-1-spaces which satisfy property (sigma-B) (property (sigma-A), sigma-sheltering (F), sigma-well-ordered (F)) is hereditarily a D-space. If (X, T) satisfies omega(1)-sheltering (F), then (X, T-omega) is hereditarily a D-space. We show that if a space Xsatisfie s omega(1)-sheltering (F) and every countable discrete subspace of Xis closed, then Xis hereditarily a D-space. This gives a partial answer to a question posed by Z.Q. Feng and J.E. Porter in 2015. We finally give examples to show that there exists a space which has property (sigma-A) but it does not have a point-countable base and there exists a space which has property (C) but it does not have property (sigma-A). (C) 2020 Elsevier B.V. All rights reserved.
关键词 ：
Collins-Roscoe property Collins-Roscoe property D-space D-space omega 1-sheltering (F) omega 1-sheltering (F) Property (A) Property (A) Property (sigma-A) Property (sigma-A) Property (sigma-B) Property (sigma-B)
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| GB/T 7714 | Peng, Liang-Xue , Wang, Huan . A study on D-spaces and the metrizability of compact spaces with property (sigma-A) [J]. | TOPOLOGY AND ITS APPLICATIONS , 2021 , 301 . |
| MLA | Peng, Liang-Xue 等. "A study on D-spaces and the metrizability of compact spaces with property (sigma-A)" . | TOPOLOGY AND ITS APPLICATIONS 301 (2021) . |
| APA | Peng, Liang-Xue , Wang, Huan . A study on D-spaces and the metrizability of compact spaces with property (sigma-A) . | TOPOLOGY AND ITS APPLICATIONS , 2021 , 301 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
In this article, we mainly show that a finite product of ordinals is hereditarily dually discrete. This gives an affirmative answer to a problem posed by Peng in [16, Problem 12]. By this conclusion and a known conclusion we have that if Y is a subspace of the product of a finitely many ordinals, then Y is hereditarily a Lindelof D-space if and only if Y has countable spread. (c) 2021 Elsevier B.V. All rights reserved.
关键词 ：
Dually discrete Dually discrete Product of ordinals Product of ordinals Stationary set Stationary set
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| GB/T 7714 | Peng, Liang-Xue . A finite product of ordinals is hereditarily dually discrete [J]. | TOPOLOGY AND ITS APPLICATIONS , 2021 , 302 . |
| MLA | Peng, Liang-Xue . "A finite product of ordinals is hereditarily dually discrete" . | TOPOLOGY AND ITS APPLICATIONS 302 (2021) . |
| APA | Peng, Liang-Xue . A finite product of ordinals is hereditarily dually discrete . | TOPOLOGY AND ITS APPLICATIONS , 2021 , 302 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
In the second part of this article, we show that if Z is a metacompact subspace of a GO-space X and U is a family of open subsets of X such that Z subset of U U then there exists a point-finite family V of open subsets of X such that Z subset of UV and V ? U. Thus every subspace Y of a GO-space X is metacompact in X if and only if Y is a metacompact subspace of X. In the third part of this article, we get the following conclusions. We show that if (X, tau, <) is a GO-space and Z is a monotonically (countably) metacompact subspace of X, then Z is monotonically (countably) metacompact in X. By this conclusion we show that if (X, tau, <) is a GO-space with property (B) such that the maximal dense in itself set Z of X is a monotonically (countably) metacompact subspace of X, then X is monotonically (countably) metacompact. This gives a partial answer to [8, Question]. In the fourth part of this article, we show that if X is in PIGO and X is a countable unions of D-spaces, then X is a D-space, where PIGO is the class of perfect images of GO-spaces. In the last part of this article we point out that there is an error in the proof of Theorem 10 in (2018) [23]. Then we finally give a new proof for it. (c) 2021 Elsevier B.V. All rights reserved.
关键词 ：
D-space D-space GO-space GO-space metacompact metacompact Monotonically (countably) Monotonically (countably) Property (B) Property (B)
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| GB/T 7714 | Peng, Liang-Xue , Ma, Chun-Jie , Wang, Li-Jun . On (monotonically) metacompact subspaces of GO-spaces and related conclusions & nbsp; [J]. | TOPOLOGY AND ITS APPLICATIONS , 2021 , 295 . |
| MLA | Peng, Liang-Xue 等. "On (monotonically) metacompact subspaces of GO-spaces and related conclusions & nbsp;" . | TOPOLOGY AND ITS APPLICATIONS 295 (2021) . |
| APA | Peng, Liang-Xue , Ma, Chun-Jie , Wang, Li-Jun . On (monotonically) metacompact subspaces of GO-spaces and related conclusions & nbsp; . | TOPOLOGY AND ITS APPLICATIONS , 2021 , 295 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
Let gamma be an open cover of a space X. If there is a metric d on X which metrizes each member of gamma, then X is said to be gamma-metrizable. This notion was introduced and studied by M.A. Al Shumrani in [20]. We give an example to show that there is a gap in the proof of Theorem 2.1 and we give an example of a regular gamma-metrizable space which is not metrizable, showing that main Theorems 2.1 and 2.4 in Al Shumrani's article are false. We discuss some properties of gamma-metrizable spaces and get the following conclusions. If X-n is a gamma(n)-metrizable space for every n is an element of N, then the product space X = Pi(n is an element of N) X-n is gamma-metrizable for the natural open cover gamma of X. If X has a point-finite open cover by semi-stratifiable subspaces of X, then X is semi-stratifiable. Hence X is a semi-stratifiable space if X is a metacompact gamma-metrizable space. If X is a regular gamma-metrizable space and the family gamma is a sigma-HCP open cover of X, then X is metrizable. A space X is metrizable if and only if X is a paracompact gamma-metrizable space. Every D-space X with a sigma-weakly hereditarily closure-preserving network is a D-space. We finally get that if X is a gamma-metrizable space and the family gamma is a sigma-weakly hereditarily closure-preserving open cover of X, then X is a D-space. (C) 2020 Elsevier B.V. All rights reserved.
关键词 ：
D-space D-space gamma-metrizable gamma-metrizable Hereditarily closure-preserving Hereditarily closure-preserving Metrizable Metrizable Semi-stratifiable space Semi-stratifiable space
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| GB/T 7714 | Peng, Liang-Xue , Xu, Ying-Kun . A study of gamma-metrizable spaces [J]. | TOPOLOGY AND ITS APPLICATIONS , 2020 , 282 . |
| MLA | Peng, Liang-Xue 等. "A study of gamma-metrizable spaces" . | TOPOLOGY AND ITS APPLICATIONS 282 (2020) . |
| APA | Peng, Liang-Xue , Xu, Ying-Kun . A study of gamma-metrizable spaces . | TOPOLOGY AND ITS APPLICATIONS , 2020 , 282 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
We first point out that the Cauchy convergence topology which was introduced by M.H. Clapp and R.C. Shiflett is not a topology. We redefine the notion of the Cauchy convergence topology for function space. We give examples to show that under the new Cauchy convergence topology some results which appear in the article "A necessary and sufficient condition for the equivalence of the topologies of uniform and compact convergence" which is written by M.H. Clapp and R.C. Shiflett are not true. Finally, we improve part of the conclusions which appear in the article "Cauchy convergence topologies on the space of continuous functions" which is written by Zuquan Li and point out that the corresponding conclusions in it are true under the new Cauchy convergence topology by a small correction. (C) 2020 Elsevier B.V. All rights reserved.
关键词 ：
Cauchy convergence topology Cauchy convergence topology Cauchy sequence Cauchy sequence Finite-Cauchy cover Finite-Cauchy cover Uniform convergence topology Uniform convergence topology
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| GB/T 7714 | Peng, Liang-Xue , Sun, Yuan . On the modifications of the Cauchy convergence topology [J]. | TOPOLOGY AND ITS APPLICATIONS , 2020 , 275 . |
| MLA | Peng, Liang-Xue 等. "On the modifications of the Cauchy convergence topology" . | TOPOLOGY AND ITS APPLICATIONS 275 (2020) . |
| APA | Peng, Liang-Xue , Sun, Yuan . On the modifications of the Cauchy convergence topology . | TOPOLOGY AND ITS APPLICATIONS , 2020 , 275 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
A topological group G is called PR-factorizable if, for every continuous function f : G -> R, one can find a perfect homomorphism p : G -> H onto a second -countable topological group H and a continuous function g : H -> R such that f = g o p. We show that a topological group G is PR-factorizable if and only if G is Lindelof feathered. We also get some other equivalent conditions for the PR-factorizability of topological groups. We show that if G is a Sanchez-Okunev complete PR-factorizable topological group, then for any continuous mapping f : G -> R there exist a Polish topological group H, a perfect homomorphism g : G -> H and a continuous function h : H -> R such that f = h o g. We finally show that if G is a Lindelof feathered topological group, then G is ech-complete if and only if G is Sanchez-Okunev complete. (c) 2020 Elsevier B.V. All rights reserved.
关键词 ：
Cech-complete Cech-complete Lindelof feathered Lindelof feathered PR-factorizable PR-factorizable Sanchez-Okunev complete Sanchez-Okunev complete Topological group Topological group
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| GB/T 7714 | Peng, Liang-Xue , Liu, Ying . On Lindelof feathered topological groups [J]. | TOPOLOGY AND ITS APPLICATIONS , 2020 , 285 . |
| MLA | Peng, Liang-Xue 等. "On Lindelof feathered topological groups" . | TOPOLOGY AND ITS APPLICATIONS 285 (2020) . |
| APA | Peng, Liang-Xue , Liu, Ying . On Lindelof feathered topological groups . | TOPOLOGY AND ITS APPLICATIONS , 2020 , 285 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
Topological base plays a foundational role in topology theory. However, few works have been done to find the minimal base, which would make us difficult to interpret the internal structure of topological spaces. To address this issue, we provide a method to convert the finite topological space into Boolean matrix and some properties of minimal base are investigated. According to the properties, an algorithm(URMB) is proposed. Subsequently, the relationship between topological space and its sub-space with respect to the base is concentrated on by Boolean matrix. Then, a fast algorithm(MMB) is presented, which can avoid a mass of redundant computations. Finally, some numerical experiments are given to show the advantage and the effectiveness of MMB compared with URMB.
关键词 ：
Algorithm Algorithm Boolean matrix Boolean matrix Finite topology Finite topology Minimal base Minimal base
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| GB/T 7714 | Lin, Yidong , Li, Jinjin , Peng, Liangxue et al. Minimal Base for Finite Topological Space by Matrix Method [J]. | FUNDAMENTA INFORMATICAE , 2020 , 174 (2) : 167-183 . |
| MLA | Lin, Yidong et al. "Minimal Base for Finite Topological Space by Matrix Method" . | FUNDAMENTA INFORMATICAE 174 . 2 (2020) : 167-183 . |
| APA | Lin, Yidong , Li, Jinjin , Peng, Liangxue , Feng, Ziqin . Minimal Base for Finite Topological Space by Matrix Method . | FUNDAMENTA INFORMATICAE , 2020 , 174 (2) , 167-183 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
In this article, we introduce two notions which are called M-omega-balancedness and C-omega-balancedness, respectively. We get the following conclusions. A regular semitopological group G is topologically isomorphic to a subgroup of the product of a family of Moore semitopological groups if and only if G is M-omega-balanced and Ir(G) <= omega. A T(1 )semitopological group G is topologically isomorphic to a subgroup of the product of a family of T-1 semitopological groups with a point-countable base if and only if G is C-w-balanced and Sm(G) <= omega. If G is a Hausdorff countably compact semitopological group with Hs(G) <= omega, then the M-omega-balancedness (C-omega-balancedness) of G implies that G is a topological group. Let G be an omega-balanced paratopological group and let e be the identity of G. We show that if for each U is an element of N(e) there exist omega-good set V is an element of N(e) with V subset of U and A subset of G such that boolean OR{g(V boolean AND V-1) : g is an element of A} = G and {g(V boolean AND V-1)V : g is an element of A} is star-countable, then G is completely omega-balanced, where N(e) is the family of open neighborhoods of e in G. (C) 2020 Elsevier B.V. All rights reserved.
关键词 ：
Moore space Moore space omega-balanced omega-balanced Paratopological group Paratopological group Point-countable base Point-countable base Semitopological group Semitopological group
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| GB/T 7714 | Peng, Liang-Xue , Zhang, Pei . On some kinds of omega-balancedness in semitopological groups [J]. | TOPOLOGY AND ITS APPLICATIONS , 2020 , 274 . |
| MLA | Peng, Liang-Xue et al. "On some kinds of omega-balancedness in semitopological groups" . | TOPOLOGY AND ITS APPLICATIONS 274 (2020) . |
| APA | Peng, Liang-Xue , Zhang, Pei . On some kinds of omega-balancedness in semitopological groups . | TOPOLOGY AND ITS APPLICATIONS , 2020 , 274 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
Let PIGO be the class of perfect images of generalized ordered (GO) spaces. We show that if X is an element of PIGO, then the following properties are equivalent: X is paracompact; X is metacompact; X is meta-Lindelof; X is subparacompact; X is submetacompact; X is weak ( delta theta) over bar -refinable; X is weak (theta) over bar -refinable; X is a D-space; X is an aD-space; X is transitively D; X is linearly D; No closed subspace of X is homeomorphic to a stationary subset of a regular uncountable cardinal; X is submeta-Lindelof. We also show that if f : X -> Y is a perfect mapping such that Y is a semi-stratifiable space and X is a T1-space with a G(delta)*-diagonal, then X is a semi-stratifiable space. Let PIGT be the class of perfect images of generalized trees with Hausdorff generalized Sorgenfrey topologies. If X is an element of PIGT and X is a k-semistratifiable (stratifiable) space, then X is metrizable. If X is an element of PIGT, then X is first-countable if and only if X has a countable pseudocharacter. If f : L -> X is a continuous irreducible mapping from a GO-space L (generalized tree L with a Hausdorff generalized Sorgenfrey topology) onto a space X with a regular G(delta)-diagonal (G(delta)-diagonal), then the space L has a regular G(delta)-diagonal (G(delta)*-diagonal). (C) 2020 Elsevier B.V. All rights reserved.
关键词 ：
Generalized Sorgenfrey topology Generalized Sorgenfrey topology Generalized tree Generalized tree Metrizable Metrizable PIGO PIGO PIGT PIGT Semi-stratifiable Semi-stratifiable Stratifiable Stratifiable
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| GB/T 7714 | Peng, Liang-Xue , Wang, Huan . On some properties of perfect images of GO-spaces and generalized trees [J]. | TOPOLOGY AND ITS APPLICATIONS , 2020 , 283 . |
| MLA | Peng, Liang-Xue et al. "On some properties of perfect images of GO-spaces and generalized trees" . | TOPOLOGY AND ITS APPLICATIONS 283 (2020) . |
| APA | Peng, Liang-Xue , Wang, Huan . On some properties of perfect images of GO-spaces and generalized trees . | TOPOLOGY AND ITS APPLICATIONS , 2020 , 283 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
In the first part of this article we give some sufficient conditions under which a bounded set in a topological space (paratopological group) X is strongly bounded in X (p-bounded in X for every p is an element of omega*). We show that if X is a first-countable topological space, then every bounded subset of X is strongly bounded in X. If G is a paratopological group and for every U is an element of N(e) there exists a continuous homomorphism PU: G -> H-U onto a first-countable Hausdorff paratopological group H-U such that p(U)(-1) ((V-U) over bar) subset of (U) over bar for some neighborhood V-U of the neutral element of H-U, then any bounded set in G is strongly bounded in G. We also give some sufficient conditions under which a semitopological group G satisfies that for any U is an element of N(e) there exists a continuous homomorphism p(U): G -> H-U onto a first-countable Hausdorff semitopological group H-U such that p(U)(-1) ((V-U) over bar) subset of (U) over bar for some neighborhood V-U of the neutral element of H-U. In the last part of this note, we give some equivalent conditions for a bounded set in a Tychonoff topological space. We finally show that every pseudocompact submetacompact space is weakly Lindelof.
关键词 ：
bounded set bounded set omega-balanced omega-balanced paratopological group paratopological group p-bounded p-bounded strongly bounded set strongly bounded set strong property (*) strong property (*) weakly Lindelof space weakly Lindelof space
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| GB/T 7714 | Peng, Liang-Xue , Zhang, Pei . SOME PROPERTIES OF BOUNDED SETS IN CERTAIN TOPOLOGICAL SPACES [J]. | HOUSTON JOURNAL OF MATHEMATICS , 2019 , 45 (2) : 625-646 . |
| MLA | Peng, Liang-Xue et al. "SOME PROPERTIES OF BOUNDED SETS IN CERTAIN TOPOLOGICAL SPACES" . | HOUSTON JOURNAL OF MATHEMATICS 45 . 2 (2019) : 625-646 . |
| APA | Peng, Liang-Xue , Zhang, Pei . SOME PROPERTIES OF BOUNDED SETS IN CERTAIN TOPOLOGICAL SPACES . | HOUSTON JOURNAL OF MATHEMATICS , 2019 , 45 (2) , 625-646 . |
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