Lindelöf property and the iterated continuous function spaces

G. Sokolov

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Countably metacompact spaces in the constructible universe

Paul Szeptycki (1993)

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We present a construction from ♢* of a first countable, regular, countably metacompact space with a closed discrete subspace that is not a $G_{δ}$ . In addition some nonperfect spaces with σ-disjoint bases are constructed.

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We show that all finite powers of a Hausdorff space $X$ do not contain uncountable weakly separated subspaces iff there is a c.c.c poset $P$ such that in $V^{P}$ $X$ is a countable union of $0$ -dimensional subspaces of countable weight. We also show that this theorem is sharp in two different senses: (i) we cannot get rid of using generic extensions, (ii) we have to consider all finite powers of $X$ .

Topologies generated by closed intervals.

Kurilić, Miloš S., Pavlović, Aleksandar (2005)

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Finite union of H-sets and countable compact sets

Sylvain Kahane (1993)

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In [2], D. E. Grow and M. Insall construct a countable compact set which is not the union of two H-sets. We make precise this result in two directions, proving such a set may be, but need not be, a finite union of H-sets. Descriptive set theory tools like Cantor-Bendixson ranks are used; they are developed in the book of A. S. Kechris and A. Louveau [6]. Two proofs are presented; the first one is elementary while the second one is more general and useful. Using the last one I prove in...

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Gerald Kuba (2012)

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On D-dimension of metrizable spaces

Wojciech Olszewski (1991)

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For every cardinal τ and every ordinal α, we construct a metrizable space $M_{α} (τ)$ and a strongly countable-dimensional compact space $Z_{α} (τ)$ of weight τ such that $D (M_{α} (τ)) \leq α$ , $D (Z_{α} (τ)) \leq α$ and each metrizable space X of weight τ such that D(X) ≤ α is homeomorphic to a subspace of $M_{α} (τ)$ and to a subspace of $Z_{α + 1} (τ)$ .