| Title:
|
$C(X)$ can sometimes determine $X$ without $X$ being realcompact (English) |
| Author:
|
Henriksen, Melvin |
| Author:
|
Mitra, Biswajit |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
711-720 |
| . |
| Category:
|
math |
| . |
| Summary:
|
As usual $C(X)$ will denote the ring of real-valued continuous functions on a Tychonoff space $X$. It is well-known that if $X$ and $Y$ are realcompact spaces such that $C(X)$ and $C(Y)$ are isomorphic, then $X$ and $Y$ are homeomorphic; that is $C(X)$ {\it determines\/} $X$. The restriction to realcompact spaces stems from the fact that $C(X)$ and $C(\upsilon X)$ are isomorphic, where $\upsilon X$ is the (Hewitt) realcompactification of $X$. In this note, a class of locally compact spaces $X$ that includes properly the class of locally compact realcompact spaces is exhibited such that $C(X)$ determines $X$. The problem of getting similar results for other restricted classes of generalized realcompact spaces is posed. (English) |
| Keyword:
|
nearly realcompact space |
| Keyword:
|
fast set |
| Keyword:
|
SRM ideal |
| Keyword:
|
continuous functions with pseudocompact support |
| Keyword:
|
locally compact |
| Keyword:
|
locally pseudocompact |
| MSC:
|
46E25 |
| MSC:
|
54C35 |
| MSC:
|
54C40 |
| idZBL:
|
Zbl 1121.54035 |
| idMR:
|
MR2259501 |
| . |
| Date available:
|
2009-05-05T16:54:32Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119561 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[JM73] Johnson D., Mandelker M.: Functions with pseudocompact support.General Topology and Appl. 3 (1973), 331-338. Zbl 0277.54009, MR 0331310 |
| Reference:
|
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| Reference:
|
[Mi82] Misra P.R.: On isomorphism theorems for $C(X)$.Acta Math. Acad. Sci. Hungar. 39 (1982), 379-380. Zbl 0479.54011, MR 0653849 |
| Reference:
|
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| Reference:
|
[SS01] Schommer J., Swardson M.A.: Almost* realcompactness.Comment. Math. Univ. Carolinae 42 (2001), 385-394. MR 1832157 |
| . |
