Genus and the Lyusternik-Schnirelmann category of preimages - R. N. Karasev (Моделирование и анализ информационных систем, 2007)
In this paper some axiomatic generalization (function of open subsets) of the relative Lyusternik - Schnirelmann category is considered. For this function and a given map of the underlying space to a finite polyhedron some lower bounds on the value of this function on the preimage of some point are given.