Representing trees as relatively compact subsets of the first Baire class

S. Todorčević

Displaying similar documents to “Representing trees as relatively compact subsets of the first Baire class”

The algebraic dimension of linear metric spaces and Baire properties of their hyperspaces.

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Answering a question of Halbeisen we prove (by two different methods) that the algebraic dimension of each infinite-dimensional complete linear metric space X equals the size of X. A topological method gives a bit more: the algebraic dimension of a linear metric space X equals |X| provided the hyperspace K(X) of compact subsets of X is a Baire space. Studying the interplay between Baire properties of a linear metric space X and its hyperspace, we construct a hereditarily Baire linear...

“More or less" first-return recoverable functions.

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Balcerzak, M., Kharazishvili, A. (1999)

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Infinite combinatorics in Function spaces: Category methods

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On a class of densities of sets of positive integers.

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Universally Kuratowski–Ulam spaces

David Fremlin, Tomasz Natkaniec, Ireneusz Recław (2000)

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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: ...

Functions and Baire spaces

Zbigniew Duszyński (2011)

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Fragmentability and σ-fragmentability

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

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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 $ℓ^{\infty}$ and $ℓ_{c}^{\infty} (Γ)$ , with Γ uncountable, are determined.

Dense Continuity and Selections of Set-Valued Mappings

Kenderov, Petar, Moors, Warren, Revalski, Julian (1998)

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∗ The first and third author were partially supported by National Fund for Scientific Research at the Bulgarian Ministry of Science and Education under grant MM-701/97. A theorem proved by Fort in 1951 says that an upper or lower semi-continuous set-valued mapping from a Baire space A into non-empty compact subsets of a metric space is both lower and upper semi-continuous at the points of a dense Gδ -subset of A. In this paper we show that the conclusion of Fort’s theorem...