The genus and the Lyusternik-Schnirelmann category of preimages

Details The genus and the Lyusternik-Schnirelmann category of preimages The genus and the Lyusternik-Schnirelmann category of preimages

2010-06-16

arxiv.org/abs/1006.3144v1

R.N. Karasev. The genus and the Lyusternik-Schnirelmann category of preimages. (In Russian) // Modelirovaniye i Analiz Informa

Mathematics

Algebraic Topology

Scientific paper

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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