Separation and sober spaces in the category of quasi-proximity spaces

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Kula M., Sarac I.

FILOMAT, cilt.39, sa.33, ss.11873-11889, 2025 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 33
  • Basım Tarihi: 2025
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Scopus, Science Citation Index Expanded (SCI-EXPANDED), MathSciNet, zbMATH
  • Sayfa Sayıları: ss.11873-11889
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Erciyes Üniversitesi Adresli: Evet

Özet

The main objective of this paper is to characterize sober spaces, the separation properties T0, T′ 0 ,T0, T1, PreT2, PreT′ 2 , T2 and T′ 2 in general in the category of quasi-proximity spaces. Moreover, we introduce two notions of closure operators in the category of quasi-proximity spaces which satisfy (weak) hereditariness, productivity, idempotency and we characterize each of Ti,i = 0,1,2, quasi-proximity spaces by using these closure operators as well as show how these subcategories are related.