Connectivity properties for subspaces of function spaces determined by fixed points

Daciberg L. Gonçalves and Michael R. Kelly

Abstract and Applied Analysis, 2003, vol. 2003, issue 2, 121-128

Abstract: We study the topology of a subspace of the function space of continuous self‐mappings of a given manifold: the subspace determined by maps having the least number of fixed points in its homotopy class. In the case that the manifold is a closed disk of finite dimension, we prove that this subspace is both globally and locally path connected. We also prove this result when the manifold is a sphere of dimension 1, 3, or 7.

Date: 2003
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https://doi.org/10.1155/S1085337503204024

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2003:y:2003:i:2:p:121-128

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