Displaying similar documents to “Infinite combinatorics in Function spaces: Category methods”

Exceptional directions for Sierpiński's nonmeasurable sets

B. Kirchheim, Tomasz Natkaniec (1992)

Fundamenta Mathematicae

Similarity:

In [2] the question was considered in how many directions can a nonmeasurable plane set behave even "better" than the classical one constructed by Sierpiński in [6], in the sense that any line in a given direction intersects the set in at most one point. We considerably improve these results and give a much sharper estimate for the size of the sets of those "better" directions.

Fragmentability and σ-fragmentability

J. Jayne, I. Namioka, C. Rogers (1993)

Fundamenta Mathematicae

Similarity:

Recent work has studied the fragmentability and σ-fragmentability properties of Banach spaces. Here examples are given that justify the definitions that have been used. The fragmentability and σ-fragmentability properties of the spaces ℓ ∞ and ℓ c ∞ ( Γ ) , with Γ uncountable, are determined.

Universally Kuratowski–Ulam spaces

David Fremlin, Tomasz Natkaniec, Ireneusz Recław (2000)

Fundamenta Mathematicae

Similarity:

We introduce the notions of Kuratowski-Ulam pairs of topological spaces and universally Kuratowski-Ulam space. A pair (X,Y) of topological spaces is called a Kuratowski-Ulam pair if the Kuratowski-Ulam Theorem holds in X× Y. A space Y is called a universally Kuratowski-Ulam (uK-U) space if (X,Y) is a Kuratowski-Ulam pair for every space X. Obviously, every meager in itself space is uK-U. Moreover, it is known that every space with a countable π-basis is uK-U. We prove the following: ...