| Title:
|
On nonregular ideals and $z^\circ$-ideals in $C(X)$ (English) |
| Author:
|
Azarpanah, F. |
| Author:
|
Karavan, M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
397-407 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The spaces $X$ in which every prime $z^\circ $-ideal of $C(X)$ is either minimal or maximal are characterized. By this characterization, it turns out that for a large class of topological spaces $X$, such as metric spaces, basically disconnected spaces and one-point compactifications of discrete spaces, every prime $z^\circ $-ideal in $C(X)$ is either minimal or maximal. We will also answer the following questions: When is every nonregular prime ideal in $C(X)$ a $z^\circ $-ideal? When is every nonregular (prime) $z$-ideal in $C(X)$ a $z^\circ $-ideal? For instance, we show that every nonregular prime ideal of $C(X)$ is a $z^\circ $-ideal if and only if $X$ is a $\partial $-space (a space in which the boundary of any zeroset is contained in a zeroset with empty interior). (English) |
| Keyword:
|
$z^\circ $-ideal |
| Keyword:
|
prime $z$-ideal |
| Keyword:
|
nonregular ideal |
| Keyword:
|
almost ${P}$-space |
| Keyword:
|
$\partial $-space |
| Keyword:
|
$m$-space |
| MSC:
|
54C40 |
| idZBL:
|
Zbl 1081.54013 |
| idMR:
|
MR2137146 |
| . |
| Date available:
|
2009-09-24T11:23:52Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127986 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
