A notion of compactness in topological categories

Baran M.

PUBLICATIONES MATHEMATICAE-DEBRECEN, vol.50, pp.221-234, 1997 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 50
  • Publication Date: 1997
  • Journal Name: PUBLICATIONES MATHEMATICAE-DEBRECEN
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.221-234
  • Keywords: topological category, compact pairs, proper morphism, closed subobject, compact object
  • Erciyes University Affiliated: Yes

Abstract

In this paper, the notion of compactness as well as the notion of compact pairs for an arbitrary topological category is introduced. Furthermore, various generalizations of Tychonoff (completely regular T-1-objects) objects for an arbitrary topological category is given and the relationships among these various forms are investigated. Finally, closed and proper (perfect) morphisms are defined in an arbitrary topological category and some well-known results in the category of topological spaces are proved.