| Title:
|
Algebras and spaces of dense constancies (English) |
| Author:
|
Bella, A. |
| Author:
|
Martinez, J. |
| Author:
|
Woodward, S. D. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
449-461 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A DC-space (or space of dense constancies) is a Tychonoff space $X$ such that for each $f\in C(X)$ there is a family of open sets $\lbrace U_i\: i\in I\rbrace $, the union of which is dense in $X$, such that $f$, restricted to each $U_i$, is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean $f$-algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions are dense), and it is shown that all metrizable spaces have this property. (English) |
| Keyword:
|
space and algebra of dense constancy |
| Keyword:
|
$c$-spectrum |
| MSC:
|
06F25 |
| MSC:
|
16S90 |
| MSC:
|
54C05 |
| MSC:
|
54C35 |
| MSC:
|
54G99 |
| idZBL:
|
Zbl 1079.54506 |
| idMR:
|
MR1851539 |
| . |
| Date available:
|
2009-09-24T10:44:09Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127661 |
| . |
| 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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| . |
