Selections on $\Psi $-spaces

Michael Hrušák; Paul J. Szeptycki; Artur Hideyuki Tomita

Displaying similar documents to “Selections on $Ψ$ -spaces”

The regular topology on $C (X)$

Wolf Iberkleid, Ramiro Lafuente-Rodriguez, Warren Wm. McGovern (2011)

Commentationes Mathematicae Universitatis Carolinae

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Hewitt [Rings of real-valued continuous functions. I., Trans. Amer. Math. Soc. 64 (1948), 45–99] defined the $m$ -topology on $C (X)$ , denoted $C_{m} (X)$ , and demonstrated that certain topological properties of $X$ could be characterized by certain topological properties of $C_{m} (X)$ . For example, he showed that $X$ is pseudocompact if and only if $C_{m} (X)$ is a metrizable space; in this case the $m$ -topology is precisely the topology of uniform convergence. What is interesting with regards to the $m$ -topology is that it is...

On AP spaces in concern with compact-like sets and submaximality

Mi Ae Moon, Myung Hyun Cho, Junhui Kim (2011)

Commentationes Mathematicae Universitatis Carolinae

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The definitions of AP and WAP were originated in categorical topology by A. Pultr and A. Tozzi, Equationally closed subframes and representation of quotient spaces, Cahiers Topologie Géom. Différentielle Catég. 34 (1993), no. 3, 167-183. In general, we have the implications: $T_{2} \Rightarrow K C \Rightarrow U S \Rightarrow T_{1}$ , where $K C$ is defined as the property that every compact subset is closed and $U S$ is defined as the property that every convergent sequence has at most one limit. And a space is called submaximal if every dense subset...

On $ω^{2}$ -saturated families

Lajos Soukup (1991)

Commentationes Mathematicae Universitatis Carolinae

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If there is no inner model with measurable cardinals, then for each cardinal $λ$ there is an almost disjoint family $𝒜_{λ}$ of countable subsets of $λ$ such that every subset of $λ$ with order type $\geq ω^{2}$ contains an element of $𝒜_{λ}$ .

Weak extent in normal spaces

Ronnie Levy, Mikhail Matveev (2005)

Commentationes Mathematicae Universitatis Carolinae

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If $X$ is a space, then the $we (X)$ 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.

Displaying similar documents to “Selections on Ψ -spaces”

The regular topology on C ( X )

On AP spaces in concern with compact-like sets and submaximality

On ω 2 -saturated families

Weak extent in normal spaces

Displaying similar documents to “Selections on $Ψ$ -spaces”

The regular topology on $C (X)$

On $ω^{2}$ -saturated families