On nowhere first-countable compact spaces with countable π -weight

Jan van Mill

Commentationes Mathematicae Universitatis Carolinae (2015)

  • Volume: 56, Issue: 2, page 237-241
  • ISSN: 0010-2628

Abstract

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The minimum weight of a nowhere first-countable compact space of countable π -weight is shown to be κ B , the least cardinal κ for which the real line ℝ can be covered by κ many nowhere dense sets.

How to cite

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Mill, Jan van. "On nowhere first-countable compact spaces with countable $\pi $-weight." Commentationes Mathematicae Universitatis Carolinae 56.2 (2015): 237-241. <http://eudml.org/doc/270104>.

@article{Mill2015,
abstract = {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.},
author = {Mill, Jan van},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\pi $-weight; nowhere first-countable; $\kappa _B$; compact space},
language = {eng},
number = {2},
pages = {237-241},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On nowhere first-countable compact spaces with countable $\pi $-weight},
url = {http://eudml.org/doc/270104},
volume = {56},
year = {2015},
}

TY - JOUR
AU - Mill, Jan van
TI - On nowhere first-countable compact spaces with countable $\pi $-weight
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 2
SP - 237
EP - 241
AB - 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.
LA - eng
KW - $\pi $-weight; nowhere first-countable; $\kappa _B$; compact space
UR - http://eudml.org/doc/270104
ER -

References

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  1. Juhász I., Cardinal Functions in Topology, Mathematical Centre Tract, 34, Mathematical Centre, Amsterdam, 1971. MR0340021
  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. Zbl0798.54005MR1244377
  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. Zbl0534.03026MR0597342
  4. van Mill J., 10.1007/BF02773072, Israel J. Math. 133 (2003), 321–338. Zbl1039.54003MR1968433DOI10.1007/BF02773072
  5. Miller A.W., 10.2307/2273142, J. Symbolic Logic 47 (1982), no. 2, 275–288. Zbl0487.03026MR0654788DOI10.2307/2273142
  6. Shelah S., Covering of the null ideal may have countable cofinality, Fund. Math. 166 (2000), 109–136. Zbl0962.03046MR1804707

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