| Title:
|
Strongly base-paracompact spaces (English) |
| Author:
|
Porter, John E. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
307-314 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A space $X$ is said to be {\it strongly base-paracompact\/} if there is a basis $\Cal B$ for $X$ with $|\Cal B|=w(X)$ such that every open cover of $X$ has a star-finite open refinement by members of $\Cal B$. Strongly paracompact spaces which are strongly base-paracompact are studied. Strongly base-paracompact spaces are shown have a family of functions $\Cal{F}$ with cardinality equal to the weight such that every open cover has a locally finite partition of unity subordinated to it from $\Cal F$. (English) |
| Keyword:
|
base-paracompact |
| Keyword:
|
strongly base-paracompact |
| Keyword:
|
partition of unity |
| Keyword:
|
Lindelöf spaces |
| MSC:
|
54D20 |
| idZBL:
|
Zbl 1099.54021 |
| idMR:
|
MR2026165 |
| . |
| Date available:
|
2009-01-08T19:29:24Z |
| Last updated:
|
2020-02-20 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119387 |
| . |
| Reference:
|
[E] Engelking R.: .General Topology Heldermann Verlag, Berlin (1989). Zbl 0684.54001, MR 1039321 |
| Reference:
|
[M] Morita K.: Normal families and dimension theory for metric spaces.Math. Ann. 128 (1954), 350-362. Zbl 0057.39001, MR 0065906, 10.1007/BF01360142 |
| Reference:
|
[N] Nagata J.: On imbedding theorem for non-separable metric spaces.J. Inst. Polyt. Oasaka City Univ. 8 (1957), 128-130. Zbl 0079.38802 |
| Reference:
|
[Ny] Nyikos P.J.: Some surprising base properties in topology II.Set-theoretic Topology Papers, Inst. Medicine and Math., Ohio University, Athens Ohio, 1975-1976 Academic Press, New York (1977), 277-305. Zbl 0397.54004, MR 0442889 |
| Reference:
|
[P] Ponomarev V.I.: On the invariance of strong paracompactness under open perfect mappings.Bull. Acad. Pol. Sci. Sér. Math. 10 (1962), 425-428. MR 0142107 |
| Reference:
|
Porter J.E.: Base-paracompact spaces.to appear in Topology Appl. Zbl 1099.54021, MR 1956610 |
| . |
