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学者姓名：彭良雪
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Abstract ：
Let 9 be the class of all spaces Y satisfying:(1) Every compact subset of Y is a G delta-set;(2) If Y is countably compact, then it is locally compact;(3) Every closed Lindelof p-subspace of Y is metrizable.We show that if X is a nowhere locally compact compactly-fibered coset space and bX is a compactification of X such that the remainder bX \ X of X is in the class 9 , then bX \ X and X are separable metrizable spaces. Since spaces having a point countable base or a G delta-diagonal are in the class 9 , this generalizes results of Arhangel'skii. We obtain a number of related results, and also consider when a remainder of a space is a D-space.(c) 2023 Elsevier B.V. All rights reserved.
Keyword ：
Lindelof p-space Lindelof p-space D-space D-space Remainder Remainder Compactification Compactification Compactly-fibered coset space Compactly-fibered coset space
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| GB/T 7714 | Peng, Liang-Xue , Hu, Xing-Yu . On some properties of remainders of compactly-fibered coset spaces [J]. | TOPOLOGY AND ITS APPLICATIONS , 2023 , 342 . |
| MLA | Peng, Liang-Xue 等. "On some properties of remainders of compactly-fibered coset spaces" . | TOPOLOGY AND ITS APPLICATIONS 342 (2023) . |
| APA | Peng, Liang-Xue , Hu, Xing-Yu . On some properties of remainders of compactly-fibered coset spaces . | TOPOLOGY AND ITS APPLICATIONS , 2023 , 342 . |
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Abstract ：
In this article, we introduce a notion which is called bM-omega-balancedness for semitopological groups. We show that a semitopological group G is topologically isomorphic to a subgroup of the product of a family of metrizable semitopological groups if and only if Gis T-0 bM-omega-balanced. Thus a semitopological group Gis T-0 bM-omega-balanced if and only if Gis regular, has property (*) and countable index of regularity. The notion of property (*) is in the sense of I. Sanchez in [16]. We show that if Gis a T-0 bM-omega-balanced weakly Lindelof paratopological group with a q-point, then for every continuous real-valued function f: G -> R, there exist a continuous clopen homomorphism pi: G -> H onto a separable metrizable paratopological group Hsuch that ker(pi) is countably compact and a continuous real-valued function g: H -> R such that f = g omicron pi. We introduce the notions of M(DE)-factorizability for semitopological groups. We show that a semitopological group Gis Tychonoff and M-factorizable if and only if Gis T-0 bM-omega-balanced and has property omega-QU. If Gis a Tychonoff M-factorizable semitopological group and f: G -> H is an open continuous homomorphism onto a semitopological group Hsuch that ker(f) is countably compact, then His DE-factorizable. (c) 2023 Elsevier B.V. All rights reserved.
Keyword ：
bM-omega-balancedness bM-omega-balancedness R-factorizable R-factorizable DE-factorizable DE-factorizable M-factorizable M-factorizable Weakly Lindelof Weakly Lindelof
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| GB/T 7714 | Peng, Liang-Xue , Ma, Chun-Jie , Deng, Yu-Ming . On bM-omega-balancedness and M-factorizability of para(semi)topological groups [J]. | TOPOLOGY AND ITS APPLICATIONS , 2023 , 337 . |
| MLA | Peng, Liang-Xue 等. "On bM-omega-balancedness and M-factorizability of para(semi)topological groups" . | TOPOLOGY AND ITS APPLICATIONS 337 (2023) . |
| APA | Peng, Liang-Xue , Ma, Chun-Jie , Deng, Yu-Ming . On bM-omega-balancedness and M-factorizability of para(semi)topological groups . | TOPOLOGY AND ITS APPLICATIONS , 2023 , 337 . |
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Abstract ：
In this article we show that every weakly Lindelof topological group (regular totally omega-narrow paratopological group) with a q-point is R-factorizable. We finally show that if G is a countably weakly collectionwise normal weakly Lindelof totally omega- narrow paratopological group with a q-point, then G is R-factorizable. In the second part of this article, we show that if G is an m-factorizable topological group and K is any locally compact omega-narrow topological group, then G x K is m-factorizable. This generalizes Theorem 8.5.5(a) in [1]. We show that if G is a metrizable topological group satisfying w(G) <= ? and H is a ? fine topological group with a q-point satisfying hwl(H) <= ? , where ? > omega, then every closed subgroup of G x H is M-factorizable, where hwl(H) stands for the hereditary weakly Lindelof number of H. (C) 2022 Elsevier B.V. All rights reserved.
Keyword ：
R-factorizable R-factorizable q-Point q-Point M-factorizable M-factorizable Weakly Lindelof Weakly Lindelof m-Factorizable m-Factorizable
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| GB/T 7714 | Peng, Liang-Xue , Ma, Chun-Jie . A study on weakly Lindelof (para)topological groups with a q-point and m(M)-factorizability [J]. | TOPOLOGY AND ITS APPLICATIONS , 2022 , 319 . |
| MLA | Peng, Liang-Xue 等. "A study on weakly Lindelof (para)topological groups with a q-point and m(M)-factorizability" . | TOPOLOGY AND ITS APPLICATIONS 319 (2022) . |
| APA | Peng, Liang-Xue , Ma, Chun-Jie . A study on weakly Lindelof (para)topological groups with a q-point and m(M)-factorizability . | TOPOLOGY AND ITS APPLICATIONS , 2022 , 319 . |
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Abstract ：
In this article, we give an internal characterization of subgroups of products of semitopological groups which satisfy certain properties that imply D-property. For example, we give an internal characterization of subgroups of products of regular semitopological groups which satisfy open (G), give an internal characterization of subgroups of products of regular first-countable semitopological groups which satisfy property (sigma-A) (property (sigma-B)). Every first-countable semitopological group with Collins-Roscoe property satisfies pre-(G) and property (pre-sigma-B). We finally show that if G is a Hausdorff countably compact semitopological group with Hs(G) <= omega and G satisfies property (pre-sigma-B) (pre-(G)), then G is a topological group. (C) 2022 Elsevier B.V. All rights reserved.
Keyword ：
Projectively P Projectively P omega-Balanced omega-Balanced Open (G) Open (G) Property (sigma-A) Property (sigma-A) Semitopological group Semitopological group Property (pre-sigma-B) Property (pre-sigma-B)
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| GB/T 7714 | Peng, Liang-Xue , Liu, Ying . Projectively first-countable semitopological groups with certain D-properties [J]. | TOPOLOGY AND ITS APPLICATIONS , 2022 , 315 . |
| MLA | Peng, Liang-Xue 等. "Projectively first-countable semitopological groups with certain D-properties" . | TOPOLOGY AND ITS APPLICATIONS 315 (2022) . |
| APA | Peng, Liang-Xue , Liu, Ying . Projectively first-countable semitopological groups with certain D-properties . | TOPOLOGY AND ITS APPLICATIONS , 2022 , 315 . |
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Abstract ：
In this article, we show that if X is a monotonically normal space, then for any neighborhood assignment phi for X there exists a discrete subspace D of X such that X = (U{phi(d) : d is an element of D}) boolean OR (D) over bar and (D) over bar \ (U{phi(d) : d is an element of D}) is left-separated. A space X is called weakly dually discrete if for any neighborhood assignment phi for X there exists a discrete subspace D of X such that X = (U{phi(d) : d is an element of D}) boolean OR (D) over bar and (D) over bar \ (U{phi(d) : d is an element of D}) is a closed discrete subspace of X. We discuss some basic properties of weakly dually discrete spaces. In the last part of this article, we introduce the notions of linear dual discreteness and transitive dual discreteness. Some of their properties are discussed. We finally show that if a space X is discretely complete and X = U{X-n : n is an element of N} such that X-n is monotonically normal for each n is an element of N, then X is compact. If X is a monotonically normal space and Y is a compact T-1-space, then X x Y is dually 2-scattered. We also discuss some properties of spaces which are dually scattered with finite rank. (c) 2021 Elsevier B.V. All rights reserved.
Keyword ：
Monotonically normal Monotonically normal Left-separated Left-separated Transitively (linearly) dually discrete Transitively (linearly) dually discrete Weakly dually discrete Weakly dually discrete Dually discrete Dually discrete
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| GB/T 7714 | Peng, Liang-Xue , Yang, Zhen , Dong, Hai-Hong . On monotonically normal and transitively (linearly) dually discrete spaces [J]. | TOPOLOGY AND ITS APPLICATIONS , 2022 , 306 . |
| MLA | Peng, Liang-Xue 等. "On monotonically normal and transitively (linearly) dually discrete spaces" . | TOPOLOGY AND ITS APPLICATIONS 306 (2022) . |
| APA | Peng, Liang-Xue , Yang, Zhen , Dong, Hai-Hong . On monotonically normal and transitively (linearly) dually discrete spaces . | TOPOLOGY AND ITS APPLICATIONS , 2022 , 306 . |
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| GB/T 7714 | Liang-Xue, Peng . A note on compact-like semitopological groups (vol 11, pg 442, 2019) [J]. | CARPATHIAN MATHEMATICAL PUBLICATIONS , 2022 , 14 (1) . |
| MLA | Liang-Xue, Peng . "A note on compact-like semitopological groups (vol 11, pg 442, 2019)" . | CARPATHIAN MATHEMATICAL PUBLICATIONS 14 . 1 (2022) . |
| APA | Liang-Xue, Peng . A note on compact-like semitopological groups (vol 11, pg 442, 2019) . | CARPATHIAN MATHEMATICAL PUBLICATIONS , 2022 , 14 (1) . |
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Abstract ：
Countably sieve-complete spaces were defined by M. Michael in 1972. In this article, we introduce a notion called countably sieve -s-complete spaces. Some properties of countably sieve-complete (countably sieve -s-complete, strongly countably complete) spaces are discussed. We get the following main results.A topological group is countably sieve-complete if and only if G contains a closed countably compact subgroup H such that the quotient space G/H is completely metrizable and the canonical quotient mapping pi : G-+ G/H is closed. By the above conclusion and a known conclusion, we get that a topological group G is strongly countably complete if and only if G is countably sieve-complete. A topological group G is countably sieve -s-complete if and only if G contains a sequentially compact closed subgroup H with a countable base of open neighborhoods such that the quotient space G/H is a completely metrizable space and the canonical quotient mapping pi : G-+ G/H is closed. An w-balanced topological group G is countably sieve-complete if and only if G contains a closed countably compact invariant subgroup H such that the quotient space G/H is a completely metrizable topological group and the canonical quotient mapping pi : G-+ G/H is closed. A topological group G is w-narrow and countably sieve -s-complete if and only if G contains a sequentially compact closed invariant subgroup H with a countable base of open neighborhoods such that the quotient space G/H is a completely metrizable second-countable topological group and the canonical quotient mapping pi : G-+ G/H is closed.We show that if G is a regular countably sieve-complete semitopological group with Sm(G) < w and satisfies property (*), then G is a topological group. Every regular totally w-narrow countably sieve-complete paratopological group is a topological group.(c) 2022 Elsevier B.V. All rights reserved.
Keyword ：
Countably complete sieve Countably complete sieve Totally?-narrow Totally?-narrow q-Point q-Point Countably s-complete sieve Countably s-complete sieve Completely metrizable space Completely metrizable space (Para)topological group (Para)topological group
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| GB/T 7714 | Peng, Liang-Xue , Liu, Ying . On (para)topological groups with a countably (s-)complete sieve [J]. | TOPOLOGY AND ITS APPLICATIONS , 2022 , 322 . |
| MLA | Peng, Liang-Xue 等. "On (para)topological groups with a countably (s-)complete sieve" . | TOPOLOGY AND ITS APPLICATIONS 322 (2022) . |
| APA | Peng, Liang-Xue , Liu, Ying . On (para)topological groups with a countably (s-)complete sieve . | TOPOLOGY AND ITS APPLICATIONS , 2022 , 322 . |
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Abstract ：
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.
Keyword ：
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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Abstract ：
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.
Keyword ：
Property (sigma-B) Property (sigma-B) omega 1-sheltering (F) omega 1-sheltering (F) Collins-Roscoe property Collins-Roscoe property Property (sigma-A) Property (sigma-A) D-space D-space Property (A) Property (A)
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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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Abstract ：
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.
Keyword ：
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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