Categorically algebraic topology versus universal topology

  • Authors:
  • Sergey A. Solovyov

  • Affiliations:
  • Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlarska 2, 611 37 Brno, Czech Republic and Institute of Mathematics and Computer Science, University of Latvia, ...

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2013

Quantified Score

Hi-index 0.20

Visualization

Abstract

This paper continues to develop the theory of categorically algebraic (catalg) topology, introduced as a common framework for the majority of the existing many-valued topological settings, to provide convenient means of interaction between different approaches. Motivated by the results of universal topology of H. Herrlich, we show that a concrete category is fibre-small and topological if and only if it is concretely isomorphic to a subcategory of a category of catalg topological structures, which is definable by topological co-axioms.