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december 2019 Symmetric connectedness in $T_0$-quasi-metric spaces
Filiz Yıldız, Hans-Peter A. Künzi
Bull. Belg. Math. Soc. Simon Stevin 26(5): 659-679 (december 2019). DOI: 10.36045/bbms/1579402816

Abstract

We continue the study of asymmetry in $T_0$-quasi-metric spaces. In this context we introduce the property of symmetric connectedness for a $T_0$-quasi-metric space. We present some methods in order to find the symmetrically connected pairs of a $T_0$-quasi-metric space. We also show that the problem to determine the symmetry components of points turns out to be easier when formulated for the induced $T_0$-quasi-metric of an asymmetrically normed real vector space. In addition, as a kind of opposite to the notion of a metric space, we define antisymmetric $T_0$-quasi-metric spaces. Subsequently some useful results about antisymmetry can be emphasized by describing the property of antisymmetric connectedness for a $T_0$-quasi-metric space. Finally, we observe that there are natural relations between the theory of (anti)symmetrically connected $T_0$-quasi-metric spaces and the theory of connectedness in the sense of graph theory.

Citation

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Filiz Yıldız. Hans-Peter A. Künzi. "Symmetric connectedness in $T_0$-quasi-metric spaces." Bull. Belg. Math. Soc. Simon Stevin 26 (5) 659 - 679, december 2019. https://doi.org/10.36045/bbms/1579402816

Information

Published: december 2019
First available in Project Euclid: 19 January 2020

zbMATH: 07167750
MathSciNet: MR4053847
Digital Object Identifier: 10.36045/bbms/1579402816

Subjects:
Primary: 05C40, 54D05, 54E35

Rights: Copyright © 2019 The Belgian Mathematical Society

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Vol.26 • No. 5 • december 2019
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