| Title:
|
New properties of the concentric circle space and its applications to cardinal inequalities (English) |
| Author:
|
Sun, Shu-Hao |
| Author:
|
Choo, Koo-Guan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1991 |
| Pages:
|
395-403 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is well-known that the concentric circle space has no $G_\delta $-diagonal nor any countable point-separating open cover. In this paper, we reveal two new properties of the concentric circle space, which are the weak versions of $G_\delta $-diagonal and countable point-separating open cover. Then we introduce two new cardinal functions and sharpen some known cardinal inequalities. (English) |
| Keyword:
|
concentric circle space |
| Keyword:
|
weak $G_\delta $-diagonal |
| Keyword:
|
point-separating $^\ast $-open cover |
| Keyword:
|
cardinal function |
| MSC:
|
54A25 |
| MSC:
|
54D20 |
| MSC:
|
54G05 |
| idZBL:
|
Zbl 0772.54004 |
| idMR:
|
MR1137802 |
| . |
| Date available:
|
2009-01-08T17:45:20Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116982 |
| . |
| Reference:
|
[1] Burke D.K., Hodel R.: The number of compact subsets of a topological space.Proc. Amer. Math. Soc. 58 (1976), 363-368. Zbl 0335.54005, MR 0418014 |
| Reference:
|
[2] Engelking R.: General Topology.Warszawa, 1977. Zbl 0684.54001, MR 0500780 |
| Reference:
|
[3] Ginsburg J., Wood G.: A cardinal inequality for topological space involving closed discrete sets.Proc. Amer. Math. Soc. 64 (1977), 357-360. MR 0461407 |
| . |
