Notes on free topological vector spaces

Lin, Fucai; Liu, Chuan

doi:10.1016/j.topol.2020.107191

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2023

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Cited by 2 publications

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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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