Connectivity properties for subspaces of function spaces determined by fixed points
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503204024 |
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| _version_ | 1832556725521088512 |
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| author | Daciberg L. Gonçalves Michael R. Kelly |
| author_facet | Daciberg L. Gonçalves Michael R. Kelly |
| author_sort | Daciberg L. Gonçalves |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-135c2371555947ce9228b6f564a1db4d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-135c2371555947ce9228b6f564a1db4d2025-02-03T05:44:28ZengWileyAbstract and Applied Analysis1085-33751687-04092003-01-012003212112810.1155/S1085337503204024Connectivity properties for subspaces of function spaces determined by fixed pointsDaciberg L. Gonçalves0Michael R. Kelly1Departamento de Matemática, Instituto de Matemática e Estatistica, Universidade de São Paulo (IME-USP) Caixa Postal 66281, São Paulo, SP, BrazilDepartment of Mathematics and Computer Science, Loyola University, 6363 St. Charles Avenue, New Orleans, LA 70118, USAWe 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.http://dx.doi.org/10.1155/S1085337503204024 |
| spellingShingle | Daciberg L. Gonçalves Michael R. Kelly Connectivity properties for subspaces of function spaces determined by fixed points Abstract and Applied Analysis |
| title | Connectivity properties for subspaces of function spaces
determined by fixed points |
| title_full | Connectivity properties for subspaces of function spaces
determined by fixed points |
| title_fullStr | Connectivity properties for subspaces of function spaces
determined by fixed points |
| title_full_unstemmed | Connectivity properties for subspaces of function spaces
determined by fixed points |
| title_short | Connectivity properties for subspaces of function spaces
determined by fixed points |
| title_sort | connectivity properties for subspaces of function spaces determined by fixed points |
| url | http://dx.doi.org/10.1155/S1085337503204024 |
| work_keys_str_mv | AT daciberglgoncalves connectivitypropertiesforsubspacesoffunctionspacesdeterminedbyfixedpoints AT michaelrkelly connectivitypropertiesforsubspacesoffunctionspacesdeterminedbyfixedpoints |