Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces

Nezakat Javanshır; Filiz Yıldız

doi:10.32323/ujma.1323655

EN

Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces

Abstract

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.

Keywords

Antisymmetry component, Asymmetrically normed real vector space, Antisymmetric path, Complementary graph, Connected graph, Local antisymmetric connectedness, Symmetrization metric, Symmetric pair, $T_0$-quasi-metric

References

[1] F. Yıldız, H.-P. A. Künzi, Symmetric connectedness in T0-quasi-metric spaces, Bull. Belg. Math. Soc. Simon Stevin, 26(5), (2019), 659–679.
[2] A. Hellwig, L. Volkmann, The connectivity of a graph and its complement, Discrete Appl. Math., 156 (2008), 3325-3328.
[3] R. J. Wilson, Introduction to Graph Theory, Oliver and Boyd, Edinburgh, 1972.
[4] J. Munkres, Topology (Second ed.). Upper Saddle River, NJ: Prentice Hall, Inc. ISBN 978-0-13-181629-9., 2000.
[5] F. Yıldız, N. Javanshir, On the topological locality of antisymmetric connectedness, Filomat, 37(12) (2023), 3879–3886.
[6] S¸ . Cobzas¸, Functional Analysis in Asymmetric Normed Spaces, Frontiers in Mathematics, Springer, Basel, 2012.
[7] N. Demetriou, H.-P.A. K¨unzi, A study of quasi-pseudometrics, Hacet. J. Math. Stat., 46(1) (2017), 33-52.
[8] N. Javanshir, F. Yıldız, Symmetrically connected and antisymmetrically connected T0-quasi-metric extensions, Topology Appl., 276 (2020), 107179.
[9] H.-P.A. Künzi , V. Vajner, Weighted quasi-metrics, Annals of the New York Academy of Sciences, 728 (1994), 64–77.
[10] H.-P.A. K¨unzi, An introduction to quasi-uniform spaces, in: Beyond Topology, eds. F. Mynard and E. Pearl, Contemporary Mathematics, American Mathematical Society, 486 (2009), 239–304.

Details

Primary Language

English

Subjects

Topology

Journal Section

Research Article

Authors

Nezakat Javanshır
0000-0002-1780-4684
Türkiye

Filiz Yıldız ^*
0000-0002-2112-8949
Türkiye

Early Pub Date

September 18, 2023

Publication Date

September 30, 2023

Submission Date

July 6, 2023

Acceptance Date

September 10, 2023

Published in Issue

Year 2023 Volume: 6 Number: 3

DOI

https://doi.org/10.32323/ujma.1323655

IZ

https://izlik.org/JA22RM89UF

APA

Javanshır, N., & Yıldız, F. (2023). Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces. Universal Journal of Mathematics and Applications, 6(3), 100-105. https://doi.org/10.32323/ujma.1323655

AMA

1.Javanshır N, Yıldız F. Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces. Univ. J. Math. Appl. 2023;6(3):100-105. doi:10.32323/ujma.1323655

Chicago

Javanshır, Nezakat, and Filiz Yıldız. 2023. “Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces”. Universal Journal of Mathematics and Applications 6 (3): 100-105. https://doi.org/10.32323/ujma.1323655.

EndNote

Javanshır N, Yıldız F (September 1, 2023) Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces. Universal Journal of Mathematics and Applications 6 3 100–105.

IEEE

[1]N. Javanshır and F. Yıldız, “Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces”, Univ. J. Math. Appl., vol. 6, no. 3, pp. 100–105, Sept. 2023, doi: 10.32323/ujma.1323655.

ISNAD

Javanshır, Nezakat - Yıldız, Filiz. “Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces”. Universal Journal of Mathematics and Applications 6/3 (September 1, 2023): 100-105. https://doi.org/10.32323/ujma.1323655.

JAMA

1.Javanshır N, Yıldız F. Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces. Univ. J. Math. Appl. 2023;6:100–105.

MLA

Javanshır, Nezakat, and Filiz Yıldız. “Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces”. Universal Journal of Mathematics and Applications, vol. 6, no. 3, Sept. 2023, pp. 100-5, doi:10.32323/ujma.1323655.

Vancouver

1.Nezakat Javanshır, Filiz Yıldız. Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces. Univ. J. Math. Appl. 2023 Sep. 1;6(3):100-5. doi:10.32323/ujma.1323655