Displaying similar documents to “Pointwise convergence and the Wadge hierarchy”

Borel sets with σ-compact sections for nonseparable spaces

Petr Holický (2008)

Fundamenta Mathematicae

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We prove that every (extended) Borel subset E of X × Y, where X is complete metric and Y is Polish, can be covered by countably many extended Borel sets with compact sections if the sections E x = y ∈ Y : ( x , y ) ∈ E , x ∈ X, are σ-compact. This is a nonseparable version of a theorem of Saint Raymond. As a by-product, we get a proof of Saint Raymond’s result which does not use transfinite induction.

Choquet simplexes whose set of extreme points is K -analytic

Michel Talagrand (1985)

Annales de l'institut Fourier

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We construct a Choquet simplex K whose set of extreme points T is 𝒦 -analytic, but is not a 𝒦 -Borel set. The set T has the surprising property of being a K σ δ set in its Stone-Cech compactification. It is hence an example of a K σ δ set that is not absolute.

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...

An answer to a question of Arhangel'skii

Henryk Michalewski (2001)

Commentationes Mathematicae Universitatis Carolinae

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We prove that there exists an example of a metrizable non-discrete space X , such that C p ( X × ω ) ≈ l C p ( X ) but C p ( X × S ) ¬ ≈ l C p ( X ) where S = ( { 0 } ∪ { 1 n + 1 : n ∈ ω } ) and C p ( X ) is the space of all continuous functions from X into reals equipped with the topology of pointwise convergence. It answers a question of Arhangel’skii ([2, Problem 4]).

On analyticity in cosmic spaces

Oleg Okunev (1993)

Commentationes Mathematicae Universitatis Carolinae

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We prove that a cosmic space (= a Tychonoff space with a countable network) is analytic if it is an image of a K -analytic space under a measurable mapping. We also obtain characterizations of analyticity and σ -compactness in cosmic spaces in terms of metrizable continuous images. As an application, we show that if X is a separable metrizable space and Y is its dense subspace then the space of restricted continuous functions C p ( X ∣ Y ) is analytic iff it is a K σ δ -space iff X is σ -compact. ...