| Title:
|
Inserting measurable functions precisely (English) |
| Author:
|
Gutiérrez García, Javier |
| Author:
|
Kubiak, Tomasz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
3 |
| Year:
|
2014 |
| Pages:
|
743-749 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A family of subsets of a set is called a $\sigma $-topology if it is closed under arbitrary countable unions and arbitrary finite intersections. A $\sigma $-topology is perfect if any its member (open set) is a countable union of complements of open sets. In this paper perfect $\sigma $-topologies are characterized in terms of inserting lower and upper measurable functions. This improves upon and extends a similar result concerning perfect topologies. Combining this characterization with a $\sigma $-topological version of Katětov-Tong insertion theorem yields a Michael insertion theorem for normal and perfect $\sigma $-topological spaces. (English) |
| Keyword:
|
insertion |
| Keyword:
|
$\sigma $-topology |
| Keyword:
|
$\sigma $-ring |
| Keyword:
|
perfectness |
| Keyword:
|
normality |
| Keyword:
|
upper measurable function |
| Keyword:
|
lower measurable function |
| Keyword:
|
measurable function |
| MSC:
|
28A05 |
| MSC:
|
28A20 |
| idZBL:
|
Zbl 06391521 |
| idMR:
|
MR3298556 |
| DOI:
|
10.1007/s10587-014-0128-3 |
| . |
| Date available:
|
2014-12-19T16:06:53Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144054 |
| . |
| 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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| Reference:
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