Closure operators, irreducibility, Urysohn’s lemma, and Tietze extension theorem for proximity spaces

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Özkan S., KULA M., Kula S., Baran T. M.

Turkish Journal of Mathematics, vol.47, no.2, pp.870-882, 2023 (SCI-Expanded, Scopus, TRDizin) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.55730/1300-0098.3398
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.870-882
  • Keywords: Topological category, proximity space, closure operators, irreducible objects
  • Open Archive Collection: AVESIS Open Access Collection
  • Erciyes University Affiliated: Yes

Abstract

In this paper, we introduce two notions of closure in the category of proximity spaces which satisfy (weak) hereditariness, productivity, and idempotency, and we characterize each of Ti, i = 0, 1, 2, proximity spaces by using these closure operators and show how these subcategories are related. Furthermore, we characterize the irreducible proximity spaces and investigate the relationship among each of irreducible, connected and Ti, i = 1, 2, proximity spaces. Finally, we present Tietze extension theorem and Urysohn’s lemma for proximity spaces