Research Article
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Year 2023, , 100 - 105, 30.09.2023
https://doi.org/10.32323/ujma.1323655

Abstract

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.
  • [11] H.-P. A. K¨unzi, F. Yıldız, Extensions of T0-quasi-metrics, Acta Math. Hungar., 153(1) (2017), 196–215.
  • [12] F. Plastria, Asymmetric distances, semidirected networks and majority in Fermat-Weber problems, Ann. Oper. Res., 167 (2009), 121–155.

Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces

Year 2023, , 100 - 105, 30.09.2023
https://doi.org/10.32323/ujma.1323655

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.

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.
  • [11] H.-P. A. K¨unzi, F. Yıldız, Extensions of T0-quasi-metrics, Acta Math. Hungar., 153(1) (2017), 196–215.
  • [12] F. Plastria, Asymmetric distances, semidirected networks and majority in Fermat-Weber problems, Ann. Oper. Res., 167 (2009), 121–155.
There are 12 citations in total.

Details

Primary Language English
Subjects Topology
Journal Section Articles
Authors

Nezakat Javanshır 0000-0002-1780-4684

Filiz Yıldız 0000-0002-2112-8949

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

Cite

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 Javanshır N, Yıldız F. Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces. Univ. J. Math. Appl. September 2023;6(3):100-105. doi:10.32323/ujma.1323655
Chicago Javanshır, Nezakat, and Filiz Yıldız. “Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces”. Universal Journal of Mathematics and Applications 6, no. 3 (September 2023): 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 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, 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 2023), 100-105. https://doi.org/10.32323/ujma.1323655.
JAMA 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, 2023, pp. 100-5, doi:10.32323/ujma.1323655.
Vancouver Javanshır N, Yıldız F. Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces. Univ. J. Math. Appl. 2023;6(3):100-5.

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