The Lusternik-Schnirelmann category of metric spaces
Algebraic Topology
2014-04-21 v2 General Topology
Abstract
We extend the theory of the Lusternik-Schnirelmann category to general metric spaces by means of covers by arbitrary subsets. We also generalize the definition of the strict category weight. We show that if the Bockstein homomorphism on a metric space is non-zero, then its LS-category is at least two, and use this to compute the category of Pontryagin surfaces. Additionally, we prove that a Polish space with LS-category can be presented as the inverse limit of ANR spaces of category at most .
Keywords
Cite
@article{arxiv.1402.1875,
title = {The Lusternik-Schnirelmann category of metric spaces},
author = {Tulsi Srinivasan},
journal= {arXiv preprint arXiv:1402.1875},
year = {2014}
}