| Title:
|
A note on paratopological groups (English) |
| Author:
|
Liu, Chuan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
633-640 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, it is proved that a first-countable paratopological group has a regular $G_{\delta}$-diagonal, which gives an affirmative answer to Arhangel'skii and Burke's question [{\it Spaces with a regular $G_{\delta}$-diagonal\/}, Topology Appl. {\bf 153} (2006), 1917--1929]. If $G$ is a symmetrizable paratopological group, then $G$ is a developable space. We also discuss copies of $S_\omega$ and of $S_2$ in paratopological groups and generalize some Nyikos [{\it Metrizability and the Fréchet-Urysohn property in topological groups\/}, Proc. Amer. Math. Soc. {\bf 83} (1981), no. 4, 793--801] and Svetlichnyi [{\it Intersection of topologies and metrizability in topological groups\/}, Vestnik Moskov. Univ. Ser. I Mat. Mekh. {\bf 4} (1989), 79--81] results. (English) |
| Keyword:
|
paratopological group |
| Keyword:
|
symmetrizable spaces |
| Keyword:
|
regular $G_{\delta}$-diagonal |
| Keyword:
|
weak bases |
| Keyword:
|
Arens space |
| MSC:
|
22A30 |
| MSC:
|
54E30 |
| MSC:
|
54H13 |
| MSC:
|
54H99 |
| idZBL:
|
Zbl 1150.54036 |
| idMR:
|
MR2337418 |
| . |
| Date available:
|
2009-05-05T17:00:13Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119624 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| . |
