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- W3098580803 abstract "With any (open or closed) cover of a space T we associate certain homotopy classes of maps T into n-spheres. These homotopy invariants can be considered as obstructions for extensions of covers of a subspace A to a space X. We using these obstructions for generalizations of the classic KKM (Knaster-Kuratowski-Mazurkiewicz) and Sperner lemmas. In particular, we show that in the case when A is a k-sphere and X is a (k+1)-disk there exist KKM type lemmas for covers by n+2 sets if and only if the k-homotopy group of n-sphere is not zero." @default.
- W3098580803 created "2020-11-23" @default.
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- W3098580803 date "2016-07-01" @default.
- W3098580803 modified "2023-10-03" @default.
- W3098580803 title "Homotopy invariants of covers and KKM-type lemmas" @default.
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- W3098580803 doi "https://doi.org/10.2140/agt.2016.16.1799" @default.
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