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Addition theorems for dense subspaces

Aleksander V. Arhangel'skii (2015)

Commentationes Mathematicae Universitatis Carolinae

We study topological spaces that can be represented as the union of a finite collection of dense metrizable subspaces. The assumption that the subspaces are dense in the union plays a crucial role below. In particular, Example 3.1 shows that a paracompact space $X$ which is the union of two dense metrizable subspaces need not be a $p$ -space. However, if a normal space $X$ is the union of a finite family $μ$ of dense subspaces each of which is metrizable by a complete metric, then $X$ is also metrizable by...

Almost all submaximal groups are paracompact and σ-discrete

O. Alas, I. Protasov, M. Tkačenko, V. Tkachuk, R. Wilson, I. Yaschenko (1998)

Fundamenta Mathematicae

We prove that any topological group of a non-measurable cardinality is hereditarily paracompact and strongly σ-discrete as soon as it is submaximal. Consequently, such a group is zero-dimensional. Examples of uncountable maximal separable spaces are constructed in ZFC.

Almost closed sets and topologies they determine

Vladimir Vladimirovich Tkachuk, Ivan V. Yashchenko (2001)

Commentationes Mathematicae Universitatis Carolinae

We prove that every countably compact AP-space is Fréchet-Urysohn. It is also established that if $X$ is a paracompact space and $C_{p} (X)$ is AP, then $X$ is a Hurewicz space. We show that every scattered space is WAP and give an example of a hereditarily WAP-space which is not an AP-space.

Almost disjoint families and property (a)

Paul Szeptycki, Jerry Vaughan (1998)

Fundamenta Mathematicae

We consider the question: when does a Ψ-space satisfy property (a)? We show that if $| A | < p$ then the Ψ-space Ψ(A) satisfies property (a), but in some Cohen models the negation of CH holds and every uncountable Ψ-space fails to satisfy property (a). We also show that in a model of Fleissner and Miller there exists a Ψ-space of cardinality $p$ which has property (a). We extend a theorem of Matveev relating the existence of certain closed discrete subsets with the failure of property (a).

MSC 2010: 54A25, 54A35.

We investigate the question of the title. While it is immediate that CH yields a positive answer we discover that the situation under the negation of CH holds some surprises.

Assertion Q distinguishes topologically ω* and $𝔪$ when $𝔪$ regular and $𝔪 > ω$

R. Frankiewicz (1978)

Colloquium Mathematicae

Atomy ve svazu uniformit

Jan Reiterman, Vojtěch Rödl (1980)

Pokroky matematiky, fyziky a astronomie

Currently displaying 41 – 52 of 52

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Displaying 41 – 52 of 52

Addition theorems for dense subspaces

Almost all submaximal groups are paracompact and σ-discrete

Almost closed sets and topologies they determine

Almost disjoint families and property (a)

Amoeba relation and Galois-Tukey connections

An application of inaccessible alephs

Another Generalization of Arhangel'skii's Theorem

Application of covering sets

Approximation of $𝐑^{X}$ with countable subsets of $C_{p} (X)$ and calibers of the space $C_{p} (X)$

Are initially $ω_{1}$ -compact separable regular spaces compact?

Assertion Q distinguishes topologically ω* and $𝔪$ when $𝔪$ regular and $𝔪 > ω$

Atomy ve svazu uniformit

Currently displaying 41 – 52 of 52