A characterization of the category Q-TOP

TL;DR

This paper characterizes the category of Q-topological spaces, introduced by Solovyov, using a Sierpinski-like object, extending the classical topological space characterization to a broader algebraic context.

Contribution

It provides a new categorical characterization of Q-TOP spaces via a Sierpinski-like object, generalizing classical topological space results.

Findings

Characterization of Q-TOP category in terms of a Sierpinski-like object

Extension of classical topological space results to algebraic Q-topologies

Applicable to a large class of categories

Abstract

S.A. Solovyov (2008) has recently introduced the notion of a Q-topological space (and Q-continuous maps between them), where Q is a fixed member of a variety of Omega-algebras, which in turn gives rise to the category Q-TOP of such spaces. The purpose of this note is to give a characterization of this category (in a large class of categories), in terms of a 'Sierpinski-like' object, which is similar to the one given by E.G. Manes in 1976 for the category TOP of topological spaces.