Abstract and Applied Analysis
Volume 2003 (2003), Issue 2, Pages 121-128
Connectivity properties for subspaces of function spaces
determined by fixed points
1Departamento de Matemática, Instituto de Matemática e Estatistica, Universidade de São Paulo (IME-USP) Caixa Postal 66281, São Paulo, SP, Brazil
2Department of Mathematics and Computer Science, Loyola University, 6363 St. Charles Avenue, New Orleans 70118, LA, USA
Received 31 October 2001
Copyright © 2003 Daciberg L. Gonçalves and Michael R. Kelly. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.