Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 4

Some ordered function space topologies and ordered semi-uniformizability

Pages
1079–1091
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Then we investigate ordered semi-uniformizability of the ordered function space topologies such as compact-open (interior) and point-open (interior) ordered topologies.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, we define some Čech based ordered function space topologies and we introduce ordered semi-uniformizability.
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Key Findings & Data:In this work, we define some Čech based ordered function space topologies and we introduce ordered semi-uniformizability.
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Conclusion & Impact:Then we investigate ordered semi-uniformizability of the ordered function space topologies such as compact-open (interior) and point-open (interior) ordered topologies.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Čech closure operator · ordered topological space · preorder

Abstract

In this work, we define some Čech based ordered function space topologies and we introduce ordered semi-uniformizability. Then we investigate ordered semi-uniformizability of the ordered function space topologies such as compact-open (interior) and point-open (interior) ordered topologies.

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Cite This Article

Eroğlu, İ., Güner, E. (2022). Some ordered function space topologies and ordered semi-uniformizability. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 4, 1079–1091. https://ajindex.com/articles/529764

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References (19)

  1. D. Andrijević, M. Jelić and M. Mršević, Some properties of Hyperspaces of Čech closure spaces with Vietoris-like Topologies, Filomat, 24 (4), 53–61, 2010
  2. D. Andrijević, M. Jelić and M. Mršević, On function spaces topologies in the setting of Čech closure spaces, Topology Appl. 158, 1390–1395, 2011
  3. D.C.J. Burgess and S.D. McCartan, Order-continuous functions and order-connected spaces, Proc. Camb. Phill. Soc. 68, 27–31, 1970
  4. E. Čech, Topological spaces, Czechoslovak Acad. of Sciences, Prague, 1966
  5. İ Eroğlu and E. Güner, Separation axioms in Čech closure ordered spaces, Commun. Fac. Sci. Univ. Ank. Ser A1 Math. Stat. 65 (2), 1–10, 2016
  6. A.S. Mashhour and M.H. Ghanim, On closure spaces, Indian J. Pure Appl. Math. 14 (6), 680–691, 1983
  7. S.D. McCartan, A quotient ordered spaces, Proc. Camb. Phill. Soc. 64, 317–322, 1968 [8] S.D. McCartan, Separation axioms for topological ordered spaces, Proc. Camb. Phill. Soc. 64, 965–973, 1968
  8. S.D. McCartan, Bicontinuous preordered topological spaces, Pasific J. Math. 38, 523– 529, 1971
  9. E. Minguzzi, Normally Preordered Spaces and Utilities, Order, 30, 137–150, 2013
  10. M. Mršević, Proper and admissible topologies in closure spaces, Indian J. Pure Appl. Math. 36, 613–627, 2005
  11. M. Mršević and D. Andrijević, On θ-connectednes and θ-closure spaces, Topology Appl. 123, 157–166, 2002
  12. M. Mršević and M. Jelić, Selection principles in hyperspaces with generalized Vietoris topologies, Topology Appl. 156, 124–129, 2008
  13. L. Nachbin, Topology and order, Van Nonstrand Mathematical Studies 4, Princeton, 1965
  14. K.R. Nailana, Ordered Spaces and Quasi-Uniformities on Spaces of Continuous Order-Preserving Functions, Extracta Math. 15 (3), 513–530, 2000
  15. W. Page, Topological Uniform Structures, Dover Publications Inc. New York, 1989
  16. H.A. Priestly and B.A. Davey, Introduction to Lattices and Order, Cambridge University Press, Cambridge, 1990
  17. C.K. Rao, R. Gowri and V. Swaminathan, Čech Closure Space in Structural Configuration of Proteins, Adv. Stud. in Biol. 1 (2), 95–104, 2009
  18. J. Slapal, A digital anologue of the Jordan Curve theorem, Discrete Appl. Math. 139, 231–251, 2004
  19. J. Williams, Locally Uniform Spaces, Trans. Amer. Math. Soc. 168, 435–469, 1972.