Generalized cell structures

TL;DR

This paper introduces a generalized concept of cell structures in topology, expanding the class of spaces that can be studied through discrete approximations, including non-regular spaces.

Contribution

It weakens the original definition of cell structures and demonstrates that non-regular spaces can also admit such generalized structures.

Findings

Generalized cell structures include non-regular spaces.

The new framework broadens the applicability of cell structures in topology.

Discrete approximations can now be used for a wider class of topological spaces.

Abstract

Cell structures were introduced by W. Debski and E. Tymchatyn as a way to study some classes of topological spaces and their continuous functions by means of discrete approximations. In this work we weaken the notion of cell structure and prove that the resulting class of topological space admitting such a generalized cell structure includes non-regular spaces.