We study the behavior of the abstract sectional category in the Quillen, the Strøm and the Mixed proper model structures on topological spaces and prove that, under certain reasonable conditions, all of them coincide with the classical notion. As a result, the same conclusions hold for the abstract Lusternik-Schnirelmann category and the abstract topological complexity of a space.
Abstract sectional category in model structures on topological spaces / Moraschini M.; Murillo A.. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - STAMPA. - 199:(2016), pp. 23-31. [10.1016/j.topol.2015.12.002]
Abstract sectional category in model structures on topological spaces
Moraschini M.;
2016
Abstract
We study the behavior of the abstract sectional category in the Quillen, the Strøm and the Mixed proper model structures on topological spaces and prove that, under certain reasonable conditions, all of them coincide with the classical notion. As a result, the same conclusions hold for the abstract Lusternik-Schnirelmann category and the abstract topological complexity of a space.File in questo prodotto:
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