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 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 158 Issue: 15
  • Publication Date: 2011
  • Doi Number: 10.1016/j.topol.2011.06.043
  • Title of Journal : TOPOLOGY AND ITS APPLICATIONS
  • Page Numbers: pp.2076-2084

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.