Separation and compactness in topological categories

BARAN M.

Filomat, vol.39, no.3, pp.871-881, 2025 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 3
  • Publication Date: 2025
  • Doi Number: 10.2298/fil2503871b
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.871-881
  • Keywords: Cauchy spaces, Constant filter convergence spaces, strong closedness, strongly compact spaces, T2 spaces
  • Erciyes University Affiliated: Yes

Abstract

In previous papers, several extensions of the notions of closedness, separation properties, and compactness in a set-based topological category were introduced. In this paper, we develop further these extensions in a much larger non set-based topological categories. Moreover, we show that the categories KT2ConFCO (the category of KT2 constant filter convergence spaces and continuous functions) and Chy (the category of Cauchy spaces and Cauchy maps) are isomorphic. Also, we characterize strongly compact constant filter convergence spaces and investigate some invariance properties of them. Finally, we compare our results and give some applications.