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We construct a family of spaces with “nice” structure which is universal in the class of all compact metrizable spaces of large transfinite dimension $ω_{0}$ , or, equivalently, of small transfinite dimension $ω_{0}$ ; that is, the family consists of compact metrizable spaces whose transfinite dimension is $ω_{0}$ , and every compact metrizable space with transfinite dimension $ω_{0}$ is embeddable in a space of the family. We show that the least possible cardinality of such a universal family is equal to the least possible...

Weak calibers and the Scott-Watson theorem

Alessandro Fedeli (1996)

Czechoslovak Mathematical Journal

Weak extent in normal spaces

Ronnie Levy, Mikhail Matveev (2005)

Commentationes Mathematicae Universitatis Carolinae

If $X$ is a space, then the weak extent $we (X)$ of $X$ is the cardinal $min {α :$ If $𝒰$ is an open cover of $X$ , then there exists $A \subseteq X$ such that $| A | = α$ and $St (A, 𝒰) = X}$ . In this note, we show that if $X$ is a normal space such that $| X | = 𝔠$ and $we (X) = ω$ , then $X$ does not have a closed discrete subset of cardinality $𝔠$ . We show that this result cannot be strengthened in ZFC to get that the extent of $X$ is smaller than $𝔠$ , even if the condition that $we (X) = ω$ is replaced by the stronger condition that $X$ is separable.

Weight of a compactification and generating sets of functions

A. Caterino, M. C. Vipera (1988)

Rendiconti del Seminario Matematico della Università di Padova

Weights of denumerable topological spaces

Stanley Burris (1974)

Fundamenta Mathematicae

$α$ -point compactifications

Kost, Frank (1973)

Portugaliae mathematica

κ-compactness, extent and the Lindelöf number in LOTS

David Buhagiar, Emmanuel Chetcuti, Hans Weber (2014)

Open Mathematics

We study the behaviour of ℵ-compactness, extent and Lindelöf number in lexicographic products of linearly ordered spaces. It is seen, in particular, that for the case that all spaces are bounded all these properties behave very well when taking lexicographic products. We also give characterizations of these notions for generalized ordered spaces.

$ω$ H-sets and cardinal invariants

Alessandro Fedeli (1998)

Commentationes Mathematicae Universitatis Carolinae

A subset $A$ of a Hausdorff space $X$ is called an $ω$ H-set in $X$ if for every open family $𝒰$ in $X$ such that $A \subset ⋃ 𝒰$ there exists a countable subfamily $𝒱$ of $𝒰$ such that $A \subset ⋃ {\bar{V} : V \in 𝒱}$ . In this paper we introduce a new cardinal function $t_{s θ}$ and show that $| A | \leq 2^{t_{s θ} (X) ψ_{c} (X)}$ for every $ω$ H-set $A$ of a Hausdorff space $X$ .

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Displaying 361 – 380 of 400

Ultrafilter with $ℵ_{0}$ predecessors in Rudin-Frolík order

Ultrafilters and Darboux property of finitely additive measure

Ultraproducts and the axiom of choice

Una nota sobre espacios paracompactos.

Uncountable Powers of ... can be almost Lindelöf.

Undecidability of the existence of regular extremally disconnected S-spaces

Universal metric spaces

Universal spaces in the theory of transfinite dimension, II

Weak calibers and the Scott-Watson theorem

Weak extent in normal spaces

Weight of a compactification and generating sets of functions

Weights of denumerable topological spaces

$α$ -point compactifications

κ-compactness, extent and the Lindelöf number in LOTS

$ω$ H-sets and cardinal invariants

Бикомпактификации переферически бикомпактных пространств

Бикомпакты Фреше-Урысона: $π$ -точки и стоун-чеховские расширения

Вложения в топологические поля и построение поля, пространство которого не нормально

К теореме Балцара-Франека об отображениях экстремально несвязных бикомпактов на канторов дисконтинуум

Многообразия топологических алгебр.

Currently displaying 361 – 380 of 400