| Title:
|
On quasi-uniform space valued semi-continuous functions (English) |
| Author:
|
Kubiak, Tomasz |
| Author:
|
Vicente, María Angeles de Prada |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
125-133 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
F. van Gool [Comment. Math. Univ. Carolin. {\bf 33} (1992), 505--523] has introduced the concept of lower semicontinuity for functions with values in a quasi-uniform space $(R,\Cal U)$. This note provides a purely topological view at the basic ideas of van Gool. The lower semicontinuity of van Gool appears to be just the continuity with respect to the topology $T(\Cal U)$ generated by the quasi-uniformity $\Cal U$, so that many of his preparatory results become consequences of standard topological facts. In particular, when the order induced by $\Cal U$ makes $R$ into a continuous lattice, then $T(\Cal U)$ agrees with the Scott topology $\sigma (R)$ on $R$ and, thus, the lower semicontinuity reduces to a well known concept. (English) |
| Keyword:
|
lower semi-continuity |
| Keyword:
|
quasi-uniformity |
| Keyword:
|
continuous lattice |
| MSC:
|
06B35 |
| MSC:
|
54C08 |
| MSC:
|
54E15 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 1212.54043 |
| idMR:
|
MR2562809 |
| . |
| Date available:
|
2009-08-18T12:23:39Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133420 |
| . |
| 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:
|
[7] Nachbin L.: Topology and Order.Van Nostrand Mathematical Studies, 24, Princeton, New Jersey, 1965. Zbl 0333.54002, MR 0219042 |
| Reference:
|
[8] Page W.: Topological Uniform Structures.Dover, New York, 1989. Zbl 0734.46001, MR 1102896 |
| Reference:
|
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| Reference:
|
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| . |
