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, cilt.47, sa.2, ss.870-882, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.55730/1300-0098.3398
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.870-882
  • Anahtar Kelimeler: closure operators, irreducible objects, proximity space, Topological category
  • Erciyes Üniversitesi Adresli: Evet

Özet

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