Some remarks on topologized groups

Kočinac, Ljubiša D.R.

doi:10.2298/fil1603823k

Filomat

2016

DOI: 10.2298/fil1603823k

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Some remarks on topologized groups

Ljubiša D.R. Kočinac

Abstract: We define and study classes of topologized groups, in particular paratopological groups, related to precompactness and to several boundedness properties of topological groups and uniform spaces.

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2023

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Cited by 2 publications

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Some properties of pre-uniform spaces

Lin,

Xie,

et al. 2023

Filomat

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In this paper, we introduce the notions of pre-uniform spaces and pre-proximities and investigate some basic properties about them, where the definition of pre-uniformity here is different from the preuniformities which are studied in [1], [8] and [12], respectively. First, we prove that each pre-uniform pre-topology is regular, and give an example to show that there exists a pre-uniform structure on a finite set such that the pre-uniform pre-topology is not discrete. Moreover, we give three methods of generating (strongly) pre-uniformities, that is, the definition of a pre-base, a family of strongly pre-uniform covers, or a family of strongly pre-uniform pseudometrics. As an application, we show that each strongly pretopological group is completely regular. Finally, we pose the concept of the pre-proximity on a set and discuss some properties of the pre-proximity.

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Some properties of pre-uniform spaces

Lin,

Xie,

et al. 2023

Filomat

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On Star Selection Principles Theory

Kočinac

2023

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Some remarks on topologized groups

Abstract: We define and study classes of topologized groups, in particular paratopological groups, related to precompactness and to several boundedness properties of topological groups and uniform spaces.

Cited by 2 publications

References 14 publications

Some properties of pre-uniform spaces

Some properties of pre-uniform spaces

On Star Selection Principles Theory

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