On the topological locality of antisymmetric connectedness

Yıldız, Filiz; Javanshir, Nezakat

doi:10.2298/fil2312883y

Cited by 2 publications

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References 10 publications

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“…In the light of above considerations, for future work, let us state a few new questions using the notions introduced in [6] and [12], as follows.…”

Section: Discussionmentioning

confidence: 99%

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Various results on some asymmetric types of density

JAVANSHIR,

YILDIZ

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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The structures of symmetric connectedness and dually, antisymmetric connectedness were described and studied before, especially in terms of graph theory as the corresponding counterparts of the connectedness of a graph and the connectedness of its complementary graph. By taking into consideration the deficiencies of topological density in the context of symmetric and antisymmetric connectedness, two special kinds of density in the theory of non-metric $T_0$-quasi-metrics were introduced in the previous studies under the names symmetric density and antisymmetric density. In this paper, some crucial and useful properties of these two types of density are investigated with the help of the major results and (counter)examples peculiar to the asymmetric environment. Besides these, many further observations about the structures of symmetric and antisymmetric-density are dealt with, especially in the sense of their combinations such as products and unions through various theorems in the context of $T_0$-quasi-metrics. Also, we examine the question of under what kind of quasi-metric mapping these structures will be preserved.

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“…In the light of above considerations, for future work, let us state a few new questions using the notions introduced in [6] and [12], as follows.…”

Section: Discussionmentioning

confidence: 99%

“…All preliminary information presented in this section is taken from the references [3,[5][6][7][8]12].…”

Section: Introductionmentioning

confidence: 99%

Various results on some asymmetric types of density

JAVANSHIR,

YILDIZ

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces

JAVANSHIR,

YILDIZ

2023

Universal Journal of Mathematics and Applications

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In this paper, some properties of locally antisymmetrically connected spaces which are the localized version of the antisymmetrically connected $T_0$-quasi-metric spaces constructed as the natural counterparts of connected complementary graphs, are presented in terms of asymmetric norms. According to that, we investigated some different aspects and examples of local antisymmetric connectedness in the framework of asymmetrically normed real vector spaces. Specifically, it is proved that the structures of antisymmetric connectedness and local antisymmetric connectedness coincide for the $T_0$-quasi-metrics induced by the asymmetric norms which associate the theory of quasi-metrics with functional analysis.

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On the topological locality of antisymmetric connectedness

Cited by 2 publications

References 10 publications

Various results on some asymmetric types of density

Various results on some asymmetric types of density

Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces

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