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arXiv · 1006.3144

The genus and the Lyusternik-Schnirelmann category of preimages

R. N. Karasev
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Abstract

In this paper some axiomatic generalization (function of open subsets) of the relative Lyusternik-Schnirelmann category is considered, incorporating the sectional category and the Schwarz genus as well. For this function and a given continuous map of the underlying space to a finite-dimensional metric space some lower bounds on the value of this function on the (neighborhood of) preimage of some point are given.

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R. N. Karasev. 2010-06-16. The genus and the Lyusternik-Schnirelmann category of preimages. https://arxiv.org/abs/1006.3144

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