On the covering type of a space

TL;DR

This paper introduces the concept of covering type, a nuanced measure of a space's complexity based on coverings by contractible subspaces with contractible intersections, extending the idea beyond Lusternik-Schnirelman category.

Contribution

The paper defines and explores the covering type of a space, providing a new invariant that captures the complexity of coverings with contractible components and their intersections.

Findings

Covering type is a more subtle invariant than Lusternik-Schnirelman category.

The notion helps quantify the complexity of topological spaces.

Examples illustrating the differences between covering type and other invariants.

Abstract

We introduce the notion of the "covering type" of a space, which is more subtle that the notion of Lusternik Schnirelman category. It measures the complexity of a space which arises from coverings by contractible subspaces whose non-empty intersections are also contractible.