$C_p(I)$ is not subsequential

Viacheslav I. Malykhin

Displaying similar documents to “ $C_{p} (I)$ is not subsequential”

On AP and WAP spaces

Angelo Bella, Ivan V. Yashchenko (1999)

Commentationes Mathematicae Universitatis Carolinae

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Several remarks on the properties of approximation by points (AP) and weak approximation by points (WAP) are presented. We look in particular at their behavior in product and at their relationships with radiality, pseudoradiality and related concepts. For instance, relevant facts are: (a) There is in ZFC a product of a countable WAP space with a convergent sequence which fails to be WAP. (b) $C_{p}$ over $σ$ -compact space is AP. Therefore AP does not imply even pseudoradiality in function spaces,...

A note on condensations of $C_{p} (X)$ onto compacta

Aleksander V. Arhangel&#039;skii, Oleg I. Pavlov (2002)

Commentationes Mathematicae Universitatis Carolinae

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A condensation is a one-to-one continuous mapping onto. It is shown that the space $C_{p} (X)$ of real-valued continuous functions on $X$ in the topology of pointwise convergence very often cannot be condensed onto a compact Hausdorff space. In particular, this is so for any non-metrizable Eberlein compactum $X$ (Theorem 19). However, there exists a non-metrizable compactum $X$ such that $C_{p} (X)$ condenses onto a metrizable compactum (Theorem 10). Several curious open problems are formulated.

On embeddings into $C_{p} (X)$ where $X$ is Lindelöf

Masami Sakai (1992)

Commentationes Mathematicae Universitatis Carolinae

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A.V. Arkhangel’skii asked that, is it true that every space $Y$ of countable tightness is homeomorphic to a subspace (to a closed subspace) of $C_{p} (X)$ where $X$ is Lindelöf? $C_{p} (X)$ denotes the space of all continuous real-valued functions on a space $X$ with the topology of pointwise convergence. In this note we show that the two arrows space is a counterexample for the problem by showing that every separable compact linearly ordered topological space is second countable if it is homeomorphic to a subspace...

Displaying similar documents to “ C p ( I ) is not subsequential”

On AP and WAP spaces

A note on condensations of C p ( X ) onto compacta

On embeddings into C p ( X ) where X is Lindelöf

Displaying similar documents to “ $C_{p} (I)$ is not subsequential”

A note on condensations of $C_{p} (X)$ onto compacta

On embeddings into $C_{p} (X)$ where $X$ is Lindelöf