A textural view of the distinction between uniformities and quasi-uniformities


Oezcag S., Brown L. A.

TOPOLOGY AND ITS APPLICATIONS, vol.153, no.17, pp.3294-3307, 2006 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 153 Issue: 17
  • Publication Date: 2006
  • Doi Number: 10.1016/j.topol.2005.03.018
  • Title of Journal : TOPOLOGY AND ITS APPLICATIONS
  • Page Numbers: pp.3294-3307

Abstract

In this paper the authors consider the interplay between di-uniformities on a texture and a complementation on that texture. It is shown that with each di-uniformity corresponds a second di-uniformity, called its complement. Di-uniformities that coincide with their complement are then called complemented, and it is verified that the uniform ditopology of a complemented di-uniformity is a complemented ditopology. The connection with the uniform bicontinuity of the complement of a difunction is also considered.