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On the set of zeros of a mapping of a cylinder. (Russian. English summary) Zbl 0679.55005

The author considers a continuous map f: \(D^ m\times D^ k\to {\mathbb{R}}^ m\). A condition for stability of a closed subset \(F\subset f^{-1}(0)\) is found. This result is a generalization of another one proved by T. A. Lezina [Vestn. Leningr. Univ. 1984, No.7, Mat. Mekh. Astron. No.2, 98-101 (1984; Zbl 0541.34023)]. The proof is homological in its spirit.
Reviewer: V.L.Popov

MSC:

55N99 Homology and cohomology theories in algebraic topology
55M99 Classical topics in algebraic topology

Citations:

Zbl 0541.34023
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