| Title:
|
On nowhere first-countable compact spaces with countable $\pi$-weight (English) |
| Author:
|
Mill, Jan van |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
237-241 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The minimum weight of a nowhere first-countable compact space of countable $\pi$-weight is shown to be $\kappa_B$, the least cardinal $\kappa$ for which the real line $\mathbb R$ can be covered by $\kappa$ many nowhere dense sets. (English) |
| Keyword:
|
$\pi$-weight |
| Keyword:
|
nowhere first-countable |
| Keyword:
|
$\kappa_B$ |
| Keyword:
|
compact space |
| MSC:
|
54A25 |
| MSC:
|
54D35 |
| idZBL:
|
Zbl 06433821 |
| idMR:
|
MR3338736 |
| DOI:
|
10.14712/1213-7243.2015.121 |
| . |
| Date available:
|
2015-04-25T17:07:42Z |
| Last updated:
|
2017-08-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144244 |
| . |
| Reference:
|
[1] Juhász I.: Cardinal Functions in Topology.Mathematical Centre Tract, 34, Mathematical Centre, Amsterdam, 1971. MR 0340021 |
| Reference:
|
[2] Juhász I.: On the minimum character of points in compact spaces.Topology. Theory and applications, II (Pécs, 1989), Colloq. Math. Soc. János Bolyai, vol. 55, North-Holland, Amsterdam, 1993, pp. 365–371. Zbl 0798.54005, MR 1244377 |
| Reference:
|
[3] Kunen K.: Set Theory. An Introduction to Independence Proofs.Studies in Logic and the Foundations of Mathematics, 102, North-Holland Publishing Co., Amsterdam, 1980. Zbl 0534.03026, MR 0597342 |
| Reference:
|
[4] van Mill J.: On the character and $\pi$-weight of homogeneous compacta.Israel J. Math. 133 (2003), 321–338. Zbl 1039.54003, MR 1968433, 10.1007/BF02773072 |
| Reference:
|
[5] Miller A.W.: The Baire category theorem and cardinals of countable cofinality.J. Symbolic Logic 47 (1982), no. 2, 275–288. Zbl 0487.03026, MR 0654788, 10.2307/2273142 |
| Reference:
|
[6] Shelah S.: Covering of the null ideal may have countable cofinality.Fund. Math. 166 (2000), 109–136. Zbl 0962.03046, MR 1804707 |
| . |
