# Partitions of compact Hausdorff spaces

Fundamenta Mathematicae (1993)

- Volume: 142, Issue: 1, page 89-100
- ISSN: 0016-2736

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topGruenhage, Gary. "Partitions of compact Hausdorff spaces." Fundamenta Mathematicae 142.1 (1993): 89-100. <http://eudml.org/doc/211974>.

@article{Gruenhage1993,

abstract = {Under the assumption that the real line cannot be covered by $ω_1$-many nowhere dense sets, it is shown that (a) no Čech-complete space can be partitioned into $ω_1$-many closed nowhere dense sets; (b) no Hausdorff continuum can be partitioned into $ω_1$-many closed sets; and (c) no compact Hausdorff space can be partitioned into $ω_1$-many closed $G_δ$-sets.},

author = {Gruenhage, Gary},

journal = {Fundamenta Mathematicae},

keywords = {partitions by closed sets; MA countable},

language = {eng},

number = {1},

pages = {89-100},

title = {Partitions of compact Hausdorff spaces},

url = {http://eudml.org/doc/211974},

volume = {142},

year = {1993},

}

TY - JOUR

AU - Gruenhage, Gary

TI - Partitions of compact Hausdorff spaces

JO - Fundamenta Mathematicae

PY - 1993

VL - 142

IS - 1

SP - 89

EP - 100

AB - Under the assumption that the real line cannot be covered by $ω_1$-many nowhere dense sets, it is shown that (a) no Čech-complete space can be partitioned into $ω_1$-many closed nowhere dense sets; (b) no Hausdorff continuum can be partitioned into $ω_1$-many closed sets; and (c) no compact Hausdorff space can be partitioned into $ω_1$-many closed $G_δ$-sets.

LA - eng

KW - partitions by closed sets; MA countable

UR - http://eudml.org/doc/211974

ER -

## References

top- [A1] A. V. Arkhangel'skiĭ, On the cardinality of bicompacta satisfying the first axiom of countability, Soviet Math. Dokl. 10 (1969), 951-955.
- [A2] A. V. Arkhangel'skiĭ, Theorems on the cardinality of families of sets in compact Hausdorff spaces, ibid. 17 (1976), 213-217.
- [DP] A. Dow and J. Porter, Cardinalities of H-closed spaces, Topology Proc. 7 (1982), 27-50. Zbl0569.54004
- [E] R. Engelking, General Topology, Heldermann, Berlin 1989.
- [FS] D. H. Fremlin and S. Shelah, On partitions of the real line, Israel J. Math. 32 (1979), 299-304. Zbl0413.04002
- [K] K. Kunen, Set Theory, North-Holland, Amsterdam 1980.
- [M] A. W. Miller, Covering ${2}^{\omega}$ with ${\omega}_{1}$ disjoint closed sets, in: The Kleene Symposium, J. Barwise, J. Keisler, and K. Kunen (eds.), North-Holland, 1980, 415-421.
- [N] P. J. Nyikos, A supercompact topology for trees, preprint.
- [S] W. Sierpiński, Un théorème sur les continus, Tôhoku Math. J. 13 (1918), 300-303. Zbl46.0299.03
- [SV] P. Štěpánek and P. Vopěnka, Decomposition of metric spaces into nowhere dense sets, Comment. Math. Univ. Carolin. 8 (1967), 387-404. Zbl0179.27803
- [T] S. Todorčević, Trees and linearly ordered sets, in: Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan (eds.), North-Holland, 1984, 235-293.
- [W] S. Watson, Problem Session at the Spring Topology Conference, Univ. of Calif. at Sacramento, April, 1991.

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