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学者姓名：梁海兰
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Abstract ：
定义并探讨k-结构空间范畴的概念和基础性质,证明完全正则拓扑空间范畴和仿射代数簇范畴均可视为k结构空间范畴的子范畴.同时,讨论k-结构子空间与k-结构商空间的构造,并证明这两种构造分别对应于k-结构空间范畴的等值子和余等值子.最后,刻画了k-结构空间的Zariski拓扑的不可约性,并给出子空间覆盖定理的一个新视角下的有趣证明.
Keyword ：
k-态射 k-态射 k-结构空间 k-结构空间 Zariski拓扑 Zariski拓扑 子空间覆盖定理 子空间覆盖定理
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| GB/T 7714 | 黄书棋 , 王天浩 , 梁海兰 . k-结构空间的性质及其应用 [J]. | 福州大学学报（自然科学版） , 2023 , 51 (1) : 9-12 . |
| MLA | 黄书棋 等. "k-结构空间的性质及其应用" . | 福州大学学报（自然科学版） 51 . 1 (2023) : 9-12 . |
| APA | 黄书棋 , 王天浩 , 梁海兰 . k-结构空间的性质及其应用 . | 福州大学学报（自然科学版） , 2023 , 51 (1) , 9-12 . |
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In this paper, we prove that every action of a commutative cancellative semigroup can be extended to an invertible action in some kinds of categories, and this extension has universal lifting property. And the universal extension functor preserves all limits in the categorical point of view, especially, it preserves inverse limits and products. Moreover, we give some applications in dynamical systems. (c) 2023 Elsevier B.V. All rights reserved.
Keyword ：
Inverse limit Inverse limit Semigroup action Semigroup action Universal lifting property Universal lifting property
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| GB/T 7714 | Liang, Hailan , Huang, Shu-Qi . Universal lifting properties of abelian semigroup actions [J]. | TOPOLOGY AND ITS APPLICATIONS , 2023 , 341 . |
| MLA | Liang, Hailan 等. "Universal lifting properties of abelian semigroup actions" . | TOPOLOGY AND ITS APPLICATIONS 341 (2023) . |
| APA | Liang, Hailan , Huang, Shu-Qi . Universal lifting properties of abelian semigroup actions . | TOPOLOGY AND ITS APPLICATIONS , 2023 , 341 . |
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Let pi : (T, X) -> (T, Z) be an extension of flows with phase group T. A point x in X is pi-distal if x is proximal to at most itself in pi(-1)pi x boolean AND (Tx) over bar under (T, X). We study the pi-distal points using combinatorial methods. We present characterizations of pi-distal points using product IP/C-w/C-recurrence, dynamics syndetic sets, distal sets, IP*-sets, and C*-sets in T. Moreover, we give the dynamics realization of IP-set of any discrete group by IP-recurrent point and the dynamics realization of C-set of Z(d) by C-recurrent point. The IP*-recurrence of pi-distal points introduced here is useful for simplifying the proof of Furstenberg's structure theorem. (C) 2021 Elsevier B.V. All rights reserved.
Keyword ：
C-set C-set C-w-set C-w-set Distal point Distal point Flow Flow IP-set IP-set Product recurrence Product recurrence
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| GB/T 7714 | Dai, Xiongping , Liang, Hailan , Xiao, Zubiao . Characterizations of relativized distal points of topological dynamical systems [J]. | TOPOLOGY AND ITS APPLICATIONS , 2021 , 302 . |
| MLA | Dai, Xiongping 等. "Characterizations of relativized distal points of topological dynamical systems" . | TOPOLOGY AND ITS APPLICATIONS 302 (2021) . |
| APA | Dai, Xiongping , Liang, Hailan , Xiao, Zubiao . Characterizations of relativized distal points of topological dynamical systems . | TOPOLOGY AND ITS APPLICATIONS , 2021 , 302 . |
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| GB/T 7714 | Dai, Xiongping , Liang, Hailan . On Galvin's theorem for compact Hausdorff right-topological semigroups with dense topological centers (vol 60, pg 2421, 2017) [J]. | SCIENCE CHINA-MATHEMATICS , 2019 , 62 (12) : 2631-2632 . |
| MLA | Dai, Xiongping 等. "On Galvin's theorem for compact Hausdorff right-topological semigroups with dense topological centers (vol 60, pg 2421, 2017)" . | SCIENCE CHINA-MATHEMATICS 62 . 12 (2019) : 2631-2632 . |
| APA | Dai, Xiongping , Liang, Hailan . On Galvin's theorem for compact Hausdorff right-topological semigroups with dense topological centers (vol 60, pg 2421, 2017) . | SCIENCE CHINA-MATHEMATICS , 2019 , 62 (12) , 2631-2632 . |
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In this paper, we introduce the operator topology for the set of all continuous homomorphisms between two topological modules, and discuss the duality of topological modules over an admissible normed ring R (see Definition 2.1). We show that the dual functor B (-, R) defined on the category of locally bounded R-modules is topologically left exact. Moreover, if R is complete, and the modules are extendible, the dual functor is topologically exact. (C) 2018 Elsevier B.V. All rights reserved.
Keyword ：
Duality Duality Nonmed rings Nonmed rings Operator topology Operator topology Topological modules Topological modules
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| GB/T 7714 | Liang, Hailan , Huang, Shu-Qi . Duality of topological modules over normed rings [J]. | TOPOLOGY AND ITS APPLICATIONS , 2018 , 243 : 124-134 . |
| MLA | Liang, Hailan 等. "Duality of topological modules over normed rings" . | TOPOLOGY AND ITS APPLICATIONS 243 (2018) : 124-134 . |
| APA | Liang, Hailan , Huang, Shu-Qi . Duality of topological modules over normed rings . | TOPOLOGY AND ITS APPLICATIONS , 2018 , 243 , 124-134 . |
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In this paper, we mainly extend the Khintchine's recurrence theorem, Furstenberg's multiple recurrence theorem, and multiple Birkhoff recurrence theorem from single-valued maps to set-valued maps. (C) 2017 Elsevier Inc. All rights reserved.
Keyword ：
Multiple recurrence theorem Multiple recurrence theorem Set-valued map Set-valued map
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| GB/T 7714 | Huang, Shu-Qi , Liang, Hailan . Multiple recurrence theorems for set-valued maps [J]. | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2017 , 455 (1) : 452-462 . |
| MLA | Huang, Shu-Qi 等. "Multiple recurrence theorems for set-valued maps" . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 455 . 1 (2017) : 452-462 . |
| APA | Huang, Shu-Qi , Liang, Hailan . Multiple recurrence theorems for set-valued maps . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2017 , 455 (1) , 452-462 . |
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Keyword ：
amenable group amenable group Furstenberg correspondence principle Furstenberg correspondence principle Szemeredi theorem Szemeredi theorem
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| GB/T 7714 | Dai, Xiongping , Liang, Hailan , Tang, Xinjia . Szemeredi-type theorems for subsets of locally compact abelian groups of positive upper Banach density [J]. | ACTA ARITHMETICA , 2017 , 180 (2) : 101-109 . |
| MLA | Dai, Xiongping 等. "Szemeredi-type theorems for subsets of locally compact abelian groups of positive upper Banach density" . | ACTA ARITHMETICA 180 . 2 (2017) : 101-109 . |
| APA | Dai, Xiongping , Liang, Hailan , Tang, Xinjia . Szemeredi-type theorems for subsets of locally compact abelian groups of positive upper Banach density . | ACTA ARITHMETICA , 2017 , 180 (2) , 101-109 . |
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We generalize an important theorem of Fred Galvin from the Stone-ech compactification beta T of any discrete semigroup T to any compact Hausdorff right-topological semigroup with a dense topological center; and then apply it to Ellis' semigroups to prove that a point is distal if and only if it is IP*-recurrent, for any semiflow (T;X) with arbitrary compact Hausdorff phase space X not necessarily metrizable and with arbitrary phase semigroup T not necessarily cancelable.
Keyword ：
distal point distal point Ellis' semigroup Ellis' semigroup Galvin's theorem Galvin's theorem transformation semigroup transformation semigroup
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| GB/T 7714 | Dai, XiongPing , Liang, HaiLan . On Galvin's theorem for compact Hausdorff right-topological semigroups with dense topological centers [J]. | SCIENCE CHINA-MATHEMATICS , 2017 , 60 (12) : 2421-2428 . |
| MLA | Dai, XiongPing 等. "On Galvin's theorem for compact Hausdorff right-topological semigroups with dense topological centers" . | SCIENCE CHINA-MATHEMATICS 60 . 12 (2017) : 2421-2428 . |
| APA | Dai, XiongPing , Liang, HaiLan . On Galvin's theorem for compact Hausdorff right-topological semigroups with dense topological centers . | SCIENCE CHINA-MATHEMATICS , 2017 , 60 (12) , 2421-2428 . |
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