On the Lusternik-Schnirelmann category of Peano continua
Geometric Topology
2013-08-26 v3 General Topology
Abstract
We define the LS-category cat_g by means of covers of a space by general subsets, and show that this definition coincides with the classical Lusternik-Schnirelmann category for compact metric ANR spaces. We apply this result to give short dimension theoretic proofs of the Grossman-Whitehead theorem and Dranishnikov's theorem. We compute cat_g for some fractal Peano continua such as Menger spaces and Pontryagin surfaces.
Keywords
Cite
@article{arxiv.1212.0899,
title = {On the Lusternik-Schnirelmann category of Peano continua},
author = {Tulsi Srinivasan},
journal= {arXiv preprint arXiv:1212.0899},
year = {2013}
}