A space of small spread without the usual properties

Roitman, Judith

doi:10.1090/S0002-9939-1974-0331317-1

Proceedings of the American Mathematical Society

A space of small spread without the usual properties

Author: Judith Roitman
Journal: Proc. Amer. Math. Soc. 43 (1974), 245-248
MSC: Primary 54DXX; Secondary 54A25
DOI: https://doi.org/10.1090/S0002-9939-1974-0331317-1
MathSciNet review: 0331317
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Abstract: A space is found, for any $\alpha$ , which has spread $\alpha$ and which is not the set-theoretic union of a hereditarily $\alpha$ -Lindelof and a hereditarily $\alpha$ -separable space.

[1] A. Hajnal and I. Juhász, On hereditarily 𝛼-Lindelöf and hereditarily 𝛼-separable spaces, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 11 (1968), 115–124. MR 240779
[2] -, A consistency result concerning hereditarily $\alpha$ -separable spaces, Proceedings of the Bolyai János Mathematical Society Colloquium on Topology, Keszthely, Hungary, 1972 (to appear).