A combinatorial description of shape theory

TL;DR

This paper introduces a combinatorial approach to shape theory using finite topological T0-spaces, aiming to facilitate computational methods and defining a core concept for inverse sequences of finite spaces.

Contribution

It provides a novel combinatorial framework for shape theory and introduces the core notion for inverse sequences of finite spaces, advancing computational topology.

Findings

A combinatorial description of shape theory using finite T0-spaces.

Introduction of the core concept for inverse sequences of finite spaces.

Foundational properties of the core in finite space sequences.

Abstract

We give a combinatorial description of shape theory using finite topological $T_0$-spaces (finite partially ordered sets). This description may lead to a sort of computational shape theory. Then we introduce the notion of core for inverse sequences of finite spaces and prove some properties.