| Title:
|
Partitioning bases of topological spaces (English) |
| Author:
|
Soukup, Dániel T. |
| Author:
|
Soukup, Lajos |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
537-566 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate whether an arbitrary base for a dense-in-itself topological space can be partitioned into two bases. We prove that every base for a $T_3$ Lindelöf topology can be partitioned into two bases while there exists a consistent example of a first-countable, 0-dimensional, Hausdorff space of size $2^\omega $ and weight $\omega_1$ which admits a point countable base without a partition to two bases. (English) |
| Keyword:
|
base |
| Keyword:
|
resolvable |
| Keyword:
|
partition |
| MSC:
|
03E35 |
| MSC:
|
54A25 |
| MSC:
|
54A35 |
| idZBL:
|
Zbl 06391561 |
| idMR:
|
MR3269015 |
| . |
| Date available:
|
2014-10-09T10:01:36Z |
| Last updated:
|
2017-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143977 |
| . |
| Reference:
|
[1] Hajnal A., Hamburger P.: Set Theory.London Mathematical Society Student Texts, 48, Cambridge University Press, Cambridge, 1999, ISBN 0 521 59667 X. Zbl 0934.03057, MR 1728582 |
| Reference:
|
[2] Stone A.H.: On partitioning ordered sets into cofinal subsets.Mathematika 15 (1968), 217–222. Zbl 0164.33203, MR 0237386, 10.1112/S002557930000259X |
| . |
