| Title:
|
Some conditions under which a uniform space is fine (English) |
| Author:
|
Marconi, Umberto |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
3 |
| Year:
|
1993 |
| Pages:
|
543-547 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a uniform space of uniform weight $\mu$. It is shown that if every open covering, of power at most $\mu$, is uniform, then $X$ is fine. Furthermore, an $\omega _\mu $-metric space is fine, provided that every finite open covering is uniform. (English) |
| Keyword:
|
uniform space |
| Keyword:
|
uniform weight |
| Keyword:
|
fine uniformity |
| Keyword:
|
uniformly locally finite |
| Keyword:
|
$\omega _\mu $-additive space |
| Keyword:
|
$\omega _\mu $-metric space |
| MSC:
|
54A25 |
| MSC:
|
54A35 |
| MSC:
|
54E15 |
| idZBL:
|
Zbl 0845.54017 |
| idMR:
|
MR1243086 |
| . |
| Date available:
|
2009-01-08T18:06:04Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118611 |
| . |
| Reference:
|
[1] Artico G. and Moresco R.: $\;ømega_\mu$-additive topological spaces.Rend. Sem. Mat. Univ. Padova 67 (1982), 131-141. MR 0682706 |
| Reference:
|
[2] Atsuji M.: Uniform continuity of continuous functions of metric spaces.Pacific J. Math. 8 (1958), 11-16. Zbl 0082.16207, MR 0099023 |
| Reference:
|
[3] Di Concilio A., Naimpally S.A.: Uniform continuity in sequentially uniform spaces.Acta Mathematica Hungarica 61 3-4 (1993 \toappear). Zbl 0819.54014, MR 1200953 |
| Reference:
|
[4] Engelking R.: General Topology.Polish Scientific Publishers Warsaw (1977). Zbl 0373.54002, MR 0500780 |
| Reference:
|
[5] Isbell J.R.: Uniform Spaces.Mathematical Surveys nr 12 AMS Providence, Rhode Island (1964). Zbl 0124.15601, MR 0170323 |
| Reference:
|
[6] Isiwata T.: On uniform continuity of $C(X)$ (Japanese).Sugaku Kenkiu Roku of Tokyo Kyoiku Daigaku 2 (1955), 36-45. |
| Reference:
|
[7] Marconi U.: On the uniform paracompactness.Rend. Sem. Mat. Univ. Padova 72 (1984), 101-105. Zbl 0566.54013, MR 0778348 |
| Reference:
|
[8] Marconi U.: On uniform paracompactness of the $\;ømega_\mu$-metric spaces.Rend. Accad. Naz. Lincei 75 (1983), 102-105. MR 0780810 |
| Reference:
|
[9] Morita K.: Paracompactness and product spaces.Fund. Math. 50 (1962), 223-236. Zbl 0099.17401, MR 0132525 |
| Reference:
|
[10] Rainwater J.: Spaces whose finest uniformity is metric.Pacific J. Math. 9 (1959), 567-570. Zbl 0088.38301, MR 0106448 |
| . |
