Displaying similar documents to “The Borel structure of the collections of sub-self-similar sets and super-self-similar sets.”

Partitions of compact Hausdorff spaces

Gary Gruenhage (1993)

Fundamenta Mathematicae

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Under the assumption that the real line cannot be covered by ω 1 -many nowhere dense sets, it is shown that (a) no Čech-complete space can be partitioned into ω 1 -many closed nowhere dense sets; (b) no Hausdorff continuum can be partitioned into ω 1 -many closed sets; and (c) no compact Hausdorff space can be partitioned into ω 1 -many closed G δ -sets.

Fragmentability and σ-fragmentability

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

Fundamenta Mathematicae

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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 and c ( Γ ) , with Γ uncountable, are determined.