Partitions of compact Hausdorff spaces

• Autorzy: Gary Gruenhage
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1993
• Tom: 142
• Numer: 1
• Strony: 89-100

Daty

wydano

1993

otrzymano

1992-06-03

Twórcy

autor

Gary Gruenhage

• Department of Mathematics, Auburn University, Auburn, Alabama 36849, U.S.A.

Bibliografia

• [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.
• [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.
• [K] K. Kunen, Set Theory, North-Holland, Amsterdam 1980.
• [M] A. W. Miller, Covering $2^ω$ with $ω_1$ 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.
• [SV] P. Štěpánek and P. Vopěnka, Decomposition of metric spaces into nowhere dense sets, Comment. Math. Univ. Carolin. 8 (1967), 387-404.
• [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.