Characterizing meager paratopological groups

Banak, Taras; Guran, Igor; Ravsky, Alex

doi:10.4995/agt.2011.1698

Cited by 6 publications

(3 citation statements)

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“…Using this combinatorial characterization and the tree technique from [10], we can prove that the ideal of scattered subsets of a countable group G is coanalytic in P G . [17], every meager topological group G can be represented as the product G = CN of some countable subset C and nowhere dense subset N . Every infinite group G can be represented as a union of some countable family of small subsets [3].…”

Section: Comments and Open Questionsmentioning

confidence: 99%

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Descriptive Complexity of the Sizes of Subsets of Groups

2018

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Section: Comments and Open Questionsmentioning

confidence: 99%

“…4. By [17], every meager topological group G can be represented as the product G = CN of some countable subset C and nowhere dense subset N . Every infinite group G can be represented as a union of some countable family of small subsets [3].…”

Section: Comments and Open Questionsmentioning

confidence: 99%

Descriptive Complexity of the Sizes of Subsets of Groups

2018

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“…x → x −1 , is also continuous. The the properties of topological groups have been widely used in the study of topology, analysis and category, see [1,2,4,27,28,29,30,31,32,38,39]. For more details about topological groups, the reader see [3].…”

Section: Introductionmentioning

confidence: 99%

Some properties of Pre-topological groups

Lin¹,

Wu²,

Xie³

et al. 2022

Preprint

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In this paper, we pose the concepts of pre-topological groups and some generalizations of pre-topological groups. First, we systematically investigate some basic properties of pre-topological groups; in particular, we prove that each T 0 pre-topological group is regular and every almost topological group is completely regular which extends A.A. Markov's theorem to the class of almost topological groups. Moreover, it is shown that an almost topological group is τ -narrow if and only if it can be embedded as a subgroup of a pre-topological product of almost topological groups of weight less than or equal to τ . Finally, the cardinal invariant, the precompactness and the resolvability are investigated in the class of pre-topological groups.

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Local minimalities in paratopological groups

Lin

2014

Topology and its Applications

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Characterizing meager paratopological groups

Abstract: We prove that a Hausdorff paratopological group G is meager if and only if there are a nowhere dense subset A ⊂ G and a countable set C ⊂ G such that CA = G = AC.2010 MSC: 22A05, 22A30.

Cited by 6 publications

References 5 publications

Descriptive Complexity of the Sizes of Subsets of Groups

Descriptive Complexity of the Sizes of Subsets of Groups

Some properties of Pre-topological groups

Local minimalities in paratopological groups

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