The ideal generated by σ-nowhere dense sets
In this paper, we consider the ideal Iσ generated by all σ-nowhere dense sets in a topological space. Properties of this ideal and its relations with the Volterra property are explored. We show that Iσ is compatible with the topology for any given topological space, an analogue to the Banach categor...
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Universitat Politècnica de València
2006-10-01
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| Series: | Applied General Topology |
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| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/1928 |
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doaj-1d73e088269d4bccabfba608e77421f92020-11-24T23:47:37ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472006-10-017225326410.4995/agt.2006.19281553The ideal generated by σ-nowhere dense setsJiling Cao0Sina Greenwood1University of AucklandUniversity of AucklandIn this paper, we consider the ideal Iσ generated by all σ-nowhere dense sets in a topological space. Properties of this ideal and its relations with the Volterra property are explored. We show that Iσ is compatible with the topology for any given topological space, an analogue to the Banach category theorem. Some applications of this result and the Banach category theorem are also given.http://polipapers.upv.es/index.php/AGT/article/view/1928CompatibleIdealResolvableσ-nowhere denseVolterraWeakly Volterra |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jiling Cao Sina Greenwood |
| spellingShingle |
Jiling Cao Sina Greenwood The ideal generated by σ-nowhere dense sets Applied General Topology Compatible Ideal Resolvable σ-nowhere dense Volterra Weakly Volterra |
| author_facet |
Jiling Cao Sina Greenwood |
| author_sort |
Jiling Cao |
| title |
The ideal generated by σ-nowhere dense sets |
| title_short |
The ideal generated by σ-nowhere dense sets |
| title_full |
The ideal generated by σ-nowhere dense sets |
| title_fullStr |
The ideal generated by σ-nowhere dense sets |
| title_full_unstemmed |
The ideal generated by σ-nowhere dense sets |
| title_sort |
ideal generated by σ-nowhere dense sets |
| publisher |
Universitat Politècnica de València |
| series |
Applied General Topology |
| issn |
1576-9402 1989-4147 |
| publishDate |
2006-10-01 |
| description |
In this paper, we consider the ideal Iσ generated by all σ-nowhere dense sets in a topological space. Properties of this ideal and its relations with the Volterra property are explored. We show that Iσ is compatible with the topology for any given topological space, an analogue to the Banach category theorem. Some applications of this result and the Banach category theorem are also given. |
| topic |
Compatible Ideal Resolvable σ-nowhere dense Volterra Weakly Volterra |
| url |
http://polipapers.upv.es/index.php/AGT/article/view/1928 |
| work_keys_str_mv |
AT jilingcao theidealgeneratedbysnowheredensesets AT sinagreenwood theidealgeneratedbysnowheredensesets AT jilingcao idealgeneratedbysnowheredensesets AT sinagreenwood idealgeneratedbysnowheredensesets |
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1725488874361192448 |