Homotopy Characterization of ANR Function Spaces
Let Y be an absolute neighbourhood retract (ANR) for the class of metric spaces and let X be a topological space. Let YX denote the space of continuous maps from X to Y equipped with the compact open topology. We show that if X is a compactly generated Tychonoff space and Y is not discrete, then YX...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/925742 |
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| _version_ | 1832551437335265280 |
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| author | Jaka Smrekar |
| author_facet | Jaka Smrekar |
| author_sort | Jaka Smrekar |
| collection | DOAJ |
| description | Let Y be an absolute neighbourhood retract (ANR) for the class of metric spaces and let X be a topological space. Let YX denote the space of continuous maps from X to Y equipped with the compact open topology. We show that if X is a compactly generated Tychonoff space and Y is not discrete, then YX is an ANR for metric spaces if and only if X is hemicompact and YX has the homotopy type of a CW complex. |
| format | Article |
| id | doaj-art-0860d022a17b43b7936f2c35fe801fd5 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-0860d022a17b43b7936f2c35fe801fd52025-02-03T06:01:26ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/925742925742Homotopy Characterization of ANR Function SpacesJaka Smrekar0Fakulteta za Matematiko in Fiziko, Jadranska Ulica 19, 1111 Ljubljana, SloveniaLet Y be an absolute neighbourhood retract (ANR) for the class of metric spaces and let X be a topological space. Let YX denote the space of continuous maps from X to Y equipped with the compact open topology. We show that if X is a compactly generated Tychonoff space and Y is not discrete, then YX is an ANR for metric spaces if and only if X is hemicompact and YX has the homotopy type of a CW complex.http://dx.doi.org/10.1155/2013/925742 |
| spellingShingle | Jaka Smrekar Homotopy Characterization of ANR Function Spaces Journal of Function Spaces and Applications |
| title | Homotopy Characterization of ANR Function Spaces |
| title_full | Homotopy Characterization of ANR Function Spaces |
| title_fullStr | Homotopy Characterization of ANR Function Spaces |
| title_full_unstemmed | Homotopy Characterization of ANR Function Spaces |
| title_short | Homotopy Characterization of ANR Function Spaces |
| title_sort | homotopy characterization of anr function spaces |
| url | http://dx.doi.org/10.1155/2013/925742 |
| work_keys_str_mv | AT jakasmrekar homotopycharacterizationofanrfunctionspaces |