Statement:
Every metric space \((X,d)\) has a \(\sigma\)-point finite base.
Howard_Rubin_Number: 232
Parameter(s): This form does not depend on parameters
This form's transferability is: Unknown
This form's negation transferability is: Negation Transferable
Article Citations:
Howard-Rubin-Stanley-Keremedis-2000a: Paracompactness of metric spaces and the axiom of choice
Book references
Note connections:
Note 141
Definitions for various forms
| Howard-Rubin Number | Statement | References |
|---|---|---|
| 232 A | Every metric space has a \(\gamma\)-point finite base,for some ordinal \(\gamma\). Howard/Keremedis/slash Rubin/slashStanley [1999] and Note 141. |
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| 232 B | Every metric space has a \(\sigma\)-locally finitebase. Howard/Keremedis\slash Rubin\slash Stanley [1999] andNote 141. |
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| 232 C | Every metric space has a \(\gamma\)-locally finite base,for some ordinal \(\gamma\). Howard/slash Keremedis/slash Rubin/slashStanley [1999]and Note 141. |
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| 232 D | Every metric space \((X,d)\) has a \(\sigma\)-discretebase. Howard/Keremedis\slash Rubin/Stanley [1999] and Note 141. |
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| 232 E | Every metric space \((X,d)\) has a \(\gamma\)-discretebase, for some ordinal \(\gamma\). Howard/slash Keremedis/slashRubin/slash Stanley [1999] and Note 141. |
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| 232 F | Every metric space \((X,d)\) has a \(\sigma\)-disjointbase. Howard/Keremedis\slash Rubin/Stanley [1999] and Note 141. |
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| 232 G | Every metric space \((X,d)\) has a \(\gamma\)-disjointbase for some ordinal \(\gamma\). Howard/slash Keremedis/slashRubin/slash Stanley [1999] and Note 141. |
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| 232 H | MP: Every metric space is paracompact.Howard/Keremedis/Rubin\slash Stanley [1999] and Note 141. |
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| 232 I | Every open cover \(\cal{U}\) of a metric space \((X,d)\)has a refinement \(\cal{V}\) which covers \(X\) and which can be written as awell ordered union \(\bigcup \{V_\alpha :\alpha\in\gamma\}\) where each\(V_\alpha\) is locally finite. Howard/Keremedis/Rubin/Stanley [1999] and Note 141. |
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| 232 J | MM: Every metric space is metacompact.Howard/Keremedis/Rubin\slash Stanley [1999] and Note 141. |
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| 232 K | Every open cover \(\cal{U}\) of a metric space \((X,d)\)has a refinement \(\cal{V}\) which covers \(X\) and which can be written as awell ordered union \(\bigcup \{V_\alpha :\alpha\in\gamma\}\) where each\(V_\alpha \) is point finite. Howard/Keremedis/Rubin/Stanley [1999] and Note 141. |
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