Covering-based numbers related to the LS-category of finite spaces

TL;DR

This paper introduces new numerical invariants related to the LS-category of finite spaces, combining homotopic, graph, and hypergraph methods, along with algorithms and examples.

Contribution

It defines novel invariants based on geometric category and offers an algorithmic approach for their computation in finite spaces.

Findings

New invariants derived from geometric category

Algorithmic methods for computing these invariants

Application to examples of finite spaces

Abstract

In this paper, Lusternik-Schinrelmann and geometric category of finite spaces are considered. We define new numerical invariants of these spaces derived from the geometric category and present an algorithmic approach for its effective computation. The analysis is undertaken by combining homotopic features of the spaces, algorithms and tools from the theory of graphs and hypergraphs. We also provide a number of examples.