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Partitions of pairs of reals

Alan Taylor (1978)

Fundamenta Mathematicae

Pointwise convergence and the Wadge hierarchy

Alessandro Andretta, Alberto Marcone (2001)

Commentationes Mathematicae Universitatis Carolinae

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 of Christensen...

Possibly there is no uniformly completely Ramsey null set of size $2^{ω}$

Andrzej Nowik (2002)

Colloquium Mathematicae

We show that under the axiom $C P A_{c u b e}$ there is no uniformly completely Ramsey null set of size $2^{ω}$ . In particular, this holds in the iterated perfect set model. This answers a question of U. Darji.

Poznámka o lineární míře Vituškinových množin

Miroslav Dont (1980)

Časopis pro pěstování matematiky

Poznámka o řídkých množinách v $E_{m}$

Jan Mařík (1956)

Časopis pro pěstování matematiky

Product decomposition of a $s i g m a$ -ring

Jozef Dravecký (1985)

Mathematica Slovaca

Products of ideals of Borel sets

Gavalec, Martin (1981)

Abstracta. 9th Winter School on Abstract Analysis

Products of non- $σ$ -lower porous sets

Martin Rmoutil (2013)

Czechoslovak Mathematical Journal

In the present article we provide an example of two closed non- $σ$ -lower porous sets $A, B \subseteq ℝ$ such that the product $A \times B$ is lower porous. On the other hand, we prove the following: Let $X$ and $Y$ be topologically complete metric spaces, let $A \subseteq X$ be a non- $σ$ -lower porous Suslin set and let $B \subseteq Y$ be a non- $σ$ -porous Suslin set. Then the product $A \times B$ is non- $σ$ -lower porous. We also provide a brief summary of some basic properties of lower porosity, including a simple characterization of Suslin non- $σ$ -lower porous sets in topologically...

Properties of a function of E. Marczewski

T. Świątkowski (1978)

Fundamenta Mathematicae

Properties of measure and category in generalized Cohen's and Silver's forcing

Miroslav Repický (1987)

Acta Universitatis Carolinae. Mathematica et Physica

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