Purity of the ideal of continuous functions with pseudocompact support
Let CΨ(X) be the ideal of functions with pseudocompact support and let kX be the set of all points in υX having compact neighborhoods. We show that CΨ(X) is pure if and only if βX−kX is a round subset of βX, CΨ(X) is a projective C(X)-module if and only if CΨ(X) is pure and kX is paracompact. We a...
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Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202011067 |
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doaj-71b12d3fd8d04c34b8debd5e166e0abd2020-11-25T00:31:52ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0129738138810.1155/S0161171202011067Purity of the ideal of continuous functions with pseudocompact supportEmad A. Abu Osba0Department of Mathematics, University of Petra, Amman 961343, JordanLet CΨ(X) be the ideal of functions with pseudocompact support and let kX be the set of all points in υX having compact neighborhoods. We show that CΨ(X) is pure if and only if βX−kX is a round subset of βX, CΨ(X) is a projective C(X)-module if and only if CΨ(X) is pure and kX is paracompact. We also show that if CΨ(X) is pure, then for each f∈CΨ(X) the ideal (f) is a projective (flat) C(X)-module if and only if kX is basically disconnected (F′-space).http://dx.doi.org/10.1155/S0161171202011067 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Emad A. Abu Osba |
| spellingShingle |
Emad A. Abu Osba Purity of the ideal of continuous functions with pseudocompact support International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Emad A. Abu Osba |
| author_sort |
Emad A. Abu Osba |
| title |
Purity of the ideal of continuous functions with pseudocompact support |
| title_short |
Purity of the ideal of continuous functions with pseudocompact support |
| title_full |
Purity of the ideal of continuous functions with pseudocompact support |
| title_fullStr |
Purity of the ideal of continuous functions with pseudocompact support |
| title_full_unstemmed |
Purity of the ideal of continuous functions with pseudocompact support |
| title_sort |
purity of the ideal of continuous functions with pseudocompact support |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2002-01-01 |
| description |
Let CΨ(X) be the ideal of functions with pseudocompact
support and let kX be the set of all points in υX having compact neighborhoods. We show that
CΨ(X) is pure if and only if βX−kX is a round subset of βX, CΨ(X) is a projective C(X)-module if and
only if CΨ(X) is pure and kX is paracompact. We also show that if
CΨ(X) is
pure, then for each f∈CΨ(X) the ideal (f) is a projective (flat) C(X)-module if and only if kX is basically disconnected (F′-space). |
| url |
http://dx.doi.org/10.1155/S0161171202011067 |
| work_keys_str_mv |
AT emadaabuosba purityoftheidealofcontinuousfunctionswithpseudocompactsupport |
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1725321870544207872 |