Pointwise convergence and the Wadge hierarchy

Alessandro Andretta; Alberto Marcone

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

Borel sets with σ-compact sections for nonseparable spaces

Petr Holický (2008)

Fundamenta Mathematicae

Similarity:

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 $E_{x} = y \in Y : (x, y) \in E$ , 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

Similarity:

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

Similarity:

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

Similarity:

We prove that there exists an example of a metrizable non-discrete space $X$ , such that $C_{p} (X \times ω) \approx_{l} C_{p} (X)$ but $C_{p} (X \times S) \neg \approx_{l} C_{p} (X)$ where $S = ({0} \cup {\frac{1}{n + 1} : n \in ω})$ 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]).

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

Borel sets with σ-compact sections for nonseparable spaces

Choquet simplexes whose set of extreme points is K -analytic

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

An answer to a question of Arhangel'skii

Choquet simplexes whose set of extreme points is $K$ -analytic

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