Displaying similar documents to “On analyticity in cosmic spaces”

Descriptive properties of mappings between nonseparable Luzin spaces

Petr Holický, Václav Komínek (2007)

Czechoslovak Mathematical Journal

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We relate some subsets G of the product X × Y of nonseparable Luzin (e.g., completely metrizable) spaces to subsets H of ℕ ℕ × Y in a way which allows to deduce descriptive properties of G from corresponding theorems on H . As consequences we prove a nonseparable version of Kondô’s uniformization theorem and results on sets of points y in Y with particular properties of fibres f - 1 ( y ) of a mapping f X → Y . Using these, we get descriptions of bimeasurable mappings between nonseparable Luzin spaces in terms...

On the Lindelöf property of spaces of continuous functions over a Tychonoff space and its subspaces

Oleg Okunev (2009)

Commentationes Mathematicae Universitatis Carolinae

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We study relations between the Lindelöf property in the spaces of continuous functions with the topology of pointwise convergence over a Tychonoff space and over its subspaces. We prove, in particular, the following: a) if C p ( X ) is Lindelöf, Y = X ∪ { p } , and the point p has countable character in Y , then C p ( Y ) is Lindelöf; b) if Y is a cozero subspace of a Tychonoff space X , then l ( C p ( Y ) ω ) ≤ l ( C p ( X ) ω ) and ext ( C p ( Y ) ω ) ≤ ext ( C p ( X ) ω ) .

Pointwise convergence and the Wadge hierarchy

Alessandro Andretta, Alberto Marcone (2001)

Commentationes Mathematicae Universitatis Carolinae

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We show that if X is a Σ 1 1 separable metrizable space which is not σ -compact then C p * ( X ) , the space of bounded real-valued continuous functions on X with the topology of pointwise convergence, is Borel- Π 1 1 -complete. Assuming projective determinacy we show that if X is projective not σ -compact and n is least such that X is Σ n 1 then C p ( X ) , the space of real-valued continuous functions on X with the topology of pointwise convergence, is Borel- Π n 1 -complete. We also prove a simultaneous improvement of theorems...

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

Aleksander V. Arhangel'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.