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.
📌 3 Key Takeaways
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Objective & Hypothesis: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.
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Key Findings & Data:According to that, we investigated some different aspects and examples of local antisymmetric connectedness in the framework of asymmetrically normed real vector spaces.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Antisymmetry component · Asymmetrically normed real vector space · Antisymmetric path
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.
JAVANSHIR, N., YILDIZ, F. (2023). Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces. Universal Journal of Mathematics and Applications, Cilt: 6 Sayı: 3, 100–105. https://ajindex.com/articles/965496
F. Yıldız, H.-P. A. Künzi, Symmetric connectedness in T0-quasi-metric spaces, Bull. Belg. Math. Soc. Simon Stevin, 26(5), (2019), 659–679
A. Hellwig, L. Volkmann, The connectivity of a graph and its complement, Discrete Appl. Math., 156 (2008), 3325-3328
R. J. Wilson, Introduction to Graph Theory, Oliver and Boyd, Edinburgh, 1972
J. Munkres, Topology (Second ed.). Upper Saddle River, NJ: Prentice Hall, Inc. ISBN 978-0-13-181629-9., 2000
F. Yıldız, N. Javanshir, On the topological locality of antisymmetric connectedness, Filomat, 37(12) (2023), 3879–3886
S¸. Cobzas¸, Functional Analysis in Asymmetric Normed Spaces, Frontiers in Mathematics, Springer, Basel, 2012
N. Demetriou, H.-P.A. K¨unzi, A study of quasi-pseudometrics, Hacet. J. Math. Stat., 46(1) (2017), 33-52
N. Javanshir, F. Yıldız, Symmetrically connected and antisymmetrically connected T0-quasi-metric extensions, Topology Appl., 276 (2020), 107179
H.-P.A. Künzi, V. Vajner, Weighted quasi-metrics, Annals of the New York Academy of Sciences, 728 (1994), 64–77
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
H.-P. A. K¨unzi, F. Yıldız, Extensions of T0-quasi-metrics, Acta Math. Hungar., 153(1) (2017), 196–215
F. Plastria, Asymmetric distances, semidirected networks and majority in Fermat-Weber problems, Ann. Oper. Res., 167 (2009), 121–155.