Quotient-reflective and bireflective subcategories of the category of preordered sets

BARAN M., AL-SAFAR J.

TOPOLOGY AND ITS APPLICATIONS, vol.158, no.15, pp.2076-2084, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 158 Issue: 15
  • Publication Date: 2011
  • Doi Number: 10.1016/j.topol.2011.06.043
  • Journal Name: TOPOLOGY AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2076-2084
  • Keywords: Topological category, Closure operator, Pre-Hausdorff object, Zero-dimensional object, Preordered set
  • Erciyes University Affiliated: Yes

Abstract

In previous papers, the notions of "closedness" and "strong closedness" in set-based topological categories were introduced. In this paper, we give the characterization of closed and strongly closed subobjects of an object in the category Prord of preordered sets and show that they form appropriate closure operators which enjoy the basic properties like idempotency (weak) hereditariness, and productivity.