Finite approximation of stably compact spaces
Finite approximation of spaces by inverse sequences of graphs (in the category of so-called topological graphs) was introduced by Smyth, and developed further. The idea was subsequently taken up by Kopperman and Wilson, who developed their own purely topological approach using inverse spectra of fin...
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2002-10-01
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| Series: | Applied General Topology |
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| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/2063 |
| _version_ | 1811319089623203840 |
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| author | M.B. Smyth J. Webster |
| author_facet | M.B. Smyth J. Webster |
| author_sort | M.B. Smyth |
| collection | DOAJ |
| description | Finite approximation of spaces by inverse sequences of graphs (in the category of so-called topological graphs) was introduced by Smyth, and developed further. The idea was subsequently taken up by Kopperman and Wilson, who developed their own purely topological approach using inverse spectra of finite T0-spaces in the category of stably compact spaces. Both approaches are, however, restricted to the approximation of (compact) Hausdorff spaces and therefore cannot accommodate, for example, the upper space and (multi-) function space constructions. We present a new method of finite approximation of stably compact spaces using finite stably compact graphs, which when the topology is discrete are simply finite directed graphs. As an extended example, illustrating the problems involved, we study (ordered spaces and) arcs. |
| first_indexed | 2024-04-13T12:36:12Z |
| format | Article |
| id | doaj.art-4266db7781cf40dbbd5daf319dd09815 |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-04-13T12:36:12Z |
| publishDate | 2002-10-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-4266db7781cf40dbbd5daf319dd098152022-12-22T02:46:38ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472002-10-013219722310.4995/agt.2002.20631670Finite approximation of stably compact spacesM.B. Smyth0J. Webster1Imperial CollegeImperial CollegeFinite approximation of spaces by inverse sequences of graphs (in the category of so-called topological graphs) was introduced by Smyth, and developed further. The idea was subsequently taken up by Kopperman and Wilson, who developed their own purely topological approach using inverse spectra of finite T0-spaces in the category of stably compact spaces. Both approaches are, however, restricted to the approximation of (compact) Hausdorff spaces and therefore cannot accommodate, for example, the upper space and (multi-) function space constructions. We present a new method of finite approximation of stably compact spaces using finite stably compact graphs, which when the topology is discrete are simply finite directed graphs. As an extended example, illustrating the problems involved, we study (ordered spaces and) arcs.http://polipapers.upv.es/index.php/AGT/article/view/2063Stably compact spaceInverse limitUpper space(multi-) Function spaceLinearly ordered space |
| spellingShingle | M.B. Smyth J. Webster Finite approximation of stably compact spaces Applied General Topology Stably compact space Inverse limit Upper space (multi-) Function space Linearly ordered space |
| title | Finite approximation of stably compact spaces |
| title_full | Finite approximation of stably compact spaces |
| title_fullStr | Finite approximation of stably compact spaces |
| title_full_unstemmed | Finite approximation of stably compact spaces |
| title_short | Finite approximation of stably compact spaces |
| title_sort | finite approximation of stably compact spaces |
| topic | Stably compact space Inverse limit Upper space (multi-) Function space Linearly ordered space |
| url | http://polipapers.upv.es/index.php/AGT/article/view/2063 |
| work_keys_str_mv | AT mbsmyth finiteapproximationofstablycompactspaces AT jwebster finiteapproximationofstablycompactspaces |