Compactness, perfectness, separation, minimality and closedness with respect to closure operators

Baran M.

APPLIED CATEGORICAL STRUCTURES, vol.10, no.4, pp.403-415, 2002 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 4
  • Publication Date: 2002
  • Doi Number: 10.1023/a:1016388102703
  • Journal Name: APPLIED CATEGORICAL STRUCTURES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.403-415
  • Keywords: closure operator, topological category, convergence spaces, limit spaces, compact objects, perfect morphism
  • Erciyes University Affiliated: Yes

Abstract

In this paper, the characterization of closed and strongly closed subobjects of an object in categories of various types of filter convergence spaces is given and it is shown that they induce a notion of closure. Furthermore, each of the notions of compactness, perfectness, separation, minimality and absolute closedness with respect to these two new closure operators are characterized in these categories and some known results are re-obtained.