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学者姓名：彭良雪
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摘要 ：
Let B be a base for a nowhere locally compact Tychonoff space X and let bX be a compactification of X . Then the following two statements hold: (1) The remainder bX \ X of X is pseudocompact if and only if for any countable infinite subfamily V of B there exists an accumulation point of the family V in bX \ X . (2) If for any countable infinite subfamily V of B the set of all accumulation points of the family V in X is not a nonempty compact set of X , then bX \ X is pseudocompact. Let X = jl i is an element of I Xi be a product space and S be a subset of X satisfying the following condition: (*) For each nonempty countable set J subset of I , the projection pJ : X -> Pi i is an element of J Xi satisfies that p J ( S ) = XJ := i is an element of J X i . If B is the canonical base for X and V S = { B i boolean AND S : i is an element of omega} is a countable infinite subfamily of B S = { B boolean AND S : B is an element of B} such that the set F of all accumulation points of the family V S in S is nonempty, then for any a is an element of F there exists a countable subset J of I such that p - 1 J ( p J ( a )) boolean AND S = p - 1 J ( p J ( a )) boolean AND F and for any alpha is an element of I \ J , p alpha ( F ) = X alpha . By the above conclusions, we can get two known results in [8]. We finally show that if X = jI i is an element of I Xi is a product of a family { X i : i is an element of I } of Tychonoff spaces such that uncountably many of them are non-compact and Y is a dense subspace of X , then for every compactification bY of Y the remainder bY \ Y is pseudocompact.
关键词 ：
Pseudocompact Pseudocompact compactification compactification remainder remainder regular open set regular open set
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| GB/T 7714 | Peng, Liang-Xue , Hu, Xing-Yu . On pseudocompactness of remainders of certain spaces [J]. | FILOMAT , 2024 , 38 (20) : 7091-7099 . |
| MLA | Peng, Liang-Xue 等. "On pseudocompactness of remainders of certain spaces" . | FILOMAT 38 . 20 (2024) : 7091-7099 . |
| APA | Peng, Liang-Xue , Hu, Xing-Yu . On pseudocompactness of remainders of certain spaces . | FILOMAT , 2024 , 38 (20) , 7091-7099 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
We show that if X is a Tychonoff metacompact weakly pseudocompact countably sieve-complete space then X is & Ccaron;ech-complete. A metric space X is & Ccaron;ech-complete if and only if X is Telg & aacute;rsky complete. Then it follows that an Oxtoby complete metric space is not necessarily Telg & aacute;rsky complete. This answers Question 11.1 in [8]. We give an internal characterization of subgroups of products of first-countable semitopological groups which are paracompact sigma- spaces. We also discuss some properties of regular omega- balanced, locally omega- good semitopological groups with a qpoint, property (w*) w *) and Sm(G) ( G ) <=omega. omega. We finally give a sufficient condition under which a semitopological group is topologically isomorphic to a subgroup of a product of first-countable M 1-semitopological groups. (c) 2024 Elsevier B.V. All rights reserved.
关键词 ：
property (w & lowast;) property (w & lowast;) Paracompact sigma-space Paracompact sigma-space Countably sieve-complete Countably sieve-complete & Ccaron;ech-complete & Ccaron;ech-complete Semitopological group Semitopological group
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| GB/T 7714 | Peng, Liang-Xue , Deng, Yu-Ming . On some kinds of completeness and semitopological groups with property (w∗) [J]. | TOPOLOGY AND ITS APPLICATIONS , 2024 , 347 . |
| MLA | Peng, Liang-Xue 等. "On some kinds of completeness and semitopological groups with property (w∗)" . | TOPOLOGY AND ITS APPLICATIONS 347 (2024) . |
| APA | Peng, Liang-Xue , Deng, Yu-Ming . On some kinds of completeness and semitopological groups with property (w∗) . | TOPOLOGY AND ITS APPLICATIONS , 2024 , 347 . |
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摘要 ：
In this article, we discuss some relationships of w -balancedness and ( * ) properties which were introduced for giving characterizations of subgroups of topological products of certain para(semi)topological groups. We mainly get the following results. If G is a regular w -balanced locally w -good semitopological group with a q -point, then Ir ( G ) <= w if and only if Sm ( G ) <= w . If G is a regular strongly paracompact semitopological group with a q -point and Sm ( G ) <= w , then G is completely w - balanced if and only if G has property ( & lowast; ). If G is a regular paracompact w -balanced locally good semitopological group with a q -point and Sm ( G ) <= w , then G has property ( w * ) if and only if G has property (**). If G is a regular metacompact semitopological group with a q -point and Sm ( G ) <= w , then G is MM - w -balanced if and only if G is M - w -balanced. We show that a semitopological group G admits a homeomorphic embedding as a subgroup of a product of metrizable semitopological groups if and only if G is topologically isomorphic to a subgroup of a product of semitopological groups which are first-countable paracompact regular sigma -spaces and is topologically isomorphic to a subgroup of a product of Moore semitopological groups. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
关键词 ：
balanced Strongly metrizable space q balanced Strongly metrizable space q balancedness MM balancedness MM Completely omega Completely omega omega omega balancedness balancedness point Semitopological group M point Semitopological group M
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| GB/T 7714 | Peng, Liang-Xue . On some kinds of ω-balancedness and (*) properties in certain semitopological groups [J]. | TOPOLOGY AND ITS APPLICATIONS , 2024 , 354 . |
| MLA | Peng, Liang-Xue . "On some kinds of ω-balancedness and (*) properties in certain semitopological groups" . | TOPOLOGY AND ITS APPLICATIONS 354 (2024) . |
| APA | Peng, Liang-Xue . On some kinds of ω-balancedness and (*) properties in certain semitopological groups . | TOPOLOGY AND ITS APPLICATIONS , 2024 , 354 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
In this article, we introduce notions which are called property (c*) and property (M-3*) for semitopological groups. We show that if G is a regular semitopological group with a q-point, property (c*) and Sm(G) <= omega, then G is topologically isomorphic to a subgroup of the product of a family of first-countable M-1-semitopological groups (Nagata semitopological groups). In the third part of this article, we give an internal characterization of subgroups of product of first countable M-1-semitopological groups. A semitopological (paratopological) group G is topologically isomorphic to a subgroup of the product of a family of first-countable M-1-semitopological (paratopological) groups if and only if G satisfies the T-0 separation axiom and has property (M-3*).
关键词 ：
Nagata semitopological group Nagata semitopological group M-1-space M-1-space property (M-3*) property (M-3*) property (c*) property (c*) q-point q-point
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| GB/T 7714 | Peng, Liang-Xue . Subgroups of products of Nagata semitopological groups and related results [J]. | QUAESTIONES MATHEMATICAE , 2024 , 47 (10) : 1957-1977 . |
| MLA | Peng, Liang-Xue . "Subgroups of products of Nagata semitopological groups and related results" . | QUAESTIONES MATHEMATICAE 47 . 10 (2024) : 1957-1977 . |
| APA | Peng, Liang-Xue . Subgroups of products of Nagata semitopological groups and related results . | QUAESTIONES MATHEMATICAE , 2024 , 47 (10) , 1957-1977 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
In this article, we introduce notions which are called property (sigma-WA) (property (sigma-WB), property (WB)) with respect to a weak base B for a space X. Every T-1-space X having property (sigma-WB) with respect to a weak base B= boolean OR {B-x: x is an element of X} for X is a D-space. Every space with a point-countable weak base B= boolean OR {B-x: x is an element of X} has property (sigma-WA) (property (sigma-WB)) with respect to B. Some conclusions on D-spaces are generalized. Every T-1-space X satisfying sigma-well-ordered (wF) is a D-space. Every T-1-space X with a chain (wF) point network is a D-space. If X is a T-1-space which has property (D), then X is hereditarily a D-sigma-space. We give an example which shows that there exists a T-1-space X which has property (sigma-WB) with respect to a weak base B for X, but X does not have property (sigma-B). (c) 2022 Elsevier B.V. All rights reserved.
关键词 ：
Chain (wF) Chain (wF) Weak base Weak base Property (D) Property (D) D-space D-space Property (sigma-WA) Property (sigma-WA) Property (sigma-WB) Property (sigma-WB)
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| GB/T 7714 | Peng, Liang-Xue , Xing, Yi-Xiao . Existence of nice weak bases implies the D-property [J]. | TOPOLOGY AND ITS APPLICATIONS , 2023 , 324 . |
| MLA | Peng, Liang-Xue 等. "Existence of nice weak bases implies the D-property" . | TOPOLOGY AND ITS APPLICATIONS 324 (2023) . |
| APA | Peng, Liang-Xue , Xing, Yi-Xiao . Existence of nice weak bases implies the D-property . | TOPOLOGY AND ITS APPLICATIONS , 2023 , 324 . |
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摘要 ：
In this note, we give a definition of suitable sets for rectifiable spaces. We show that every T0 countable rectifiable space has a suitable set.
关键词 ：
Rectifiable spaces Rectifiable spaces topological group topological group suitable set suitable set
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| GB/T 7714 | Peng, Liang-Xue , Deng, Yu -Ming . On suitable sets for countable rectifiable spaces [J]. | FILOMAT , 2023 , 37 (18) : 6005-6010 . |
| MLA | Peng, Liang-Xue 等. "On suitable sets for countable rectifiable spaces" . | FILOMAT 37 . 18 (2023) : 6005-6010 . |
| APA | Peng, Liang-Xue , Deng, Yu -Ming . On suitable sets for countable rectifiable spaces . | FILOMAT , 2023 , 37 (18) , 6005-6010 . |
| 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 ：
Monotonically (countably) Monotonically (countably) metacompact metacompact Property (B) Property (B) GO-space GO-space D-space D-space
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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 . |
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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 . |
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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 ：
Stationary set Stationary set Dually discrete Dually discrete Product of ordinals Product of ordinals
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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 . |
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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 . |
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