Some categorical aspects of the inverse limits in ditopological context


YILDIZ F.

APPLIED GENERAL TOPOLOGY, vol.19, no.1, pp.101-127, 2018 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.4995/agt.2018.7812
  • Title of Journal : APPLIED GENERAL TOPOLOGY
  • Page Numbers: pp.101-127

Abstract

This paper considers some various categorical aspects of the inverse systems (projective spectrums) and inverse limits described in the category ifPDitop, whose objects are ditopological plain texture spaces and morphisms are bicontinuous point functions satisfying a compatibility condition between those spaces. In this context, the category Invinzwitop consisting of the inverse systems constructed by the objects and morphisms of ifPDitop, besides the inverse systems of mappings, described between inverse systems, is introduced, and the related ideas are studied in a categorical - functorial setting. In conclusion, an identity natural transformation is obtained in the context of inverse systems - limits constructed in ifPDitop and the ditopological infinite products are characterized by the finite products via inverse limits.