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Displaying 141 – 160 of 183

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Some complexity results in topology and analysis

Steve Jackson, R. Mauldin (1992)

Fundamenta Mathematicae

If X is a compact metric space of dimension n, then K(X), the n- dimensional kernel of X, is the union of all n-dimensional Cantor manifolds in X. Aleksandrov raised the problem of what the descriptive complexity of K(X) could be. A straightforward analysis shows that if X is an n-dimensional complete separable metric space, then K(X) is a Σ 2 1 or PCA set. We show (a) there is an n-dimensional continuum X in n + 1 for which K(X) is a complete Π 1 1 set. In particular, K ( X ) Π 1 1 - Σ 1 1 ; K(X) is coanalytic but is not an analytic...

Some topological properties of ω -covering sets

Andrzej Nowik (2000)

Czechoslovak Mathematical Journal

We prove the following theorems: There exists an ω -covering with the property s 0 . Under c o v ( 𝒩 ) = there exists X such that B o r [ B X is not an ω -covering or X B is not an ω -covering]. Also we characterize the property of being an ω -covering.

Strong measure zero and meager-additive sets through the prism of fractal measures

Ondřej Zindulka (2019)

Commentationes Mathematicae Universitatis Carolinae

We develop a theory of sharp measure zero sets that parallels Borel’s strong measure zero, and prove a theorem analogous to Galvin–Mycielski–Solovay theorem, namely that a set of reals has sharp measure zero if and only if it is meager-additive. Some consequences: A subset of 2 ω is meager-additive if and only if it is -additive; if f : 2 ω 2 ω is continuous and X is meager-additive, then so is f ( X ) .

The ideal (a) is not G δ generated

Marta Frankowska, Andrzej Nowik (2011)

Colloquium Mathematicae

We prove that the ideal (a) defined by the density topology is not G δ generated. This answers a question of Z. Grande and E. Strońska.

Currently displaying 141 – 160 of 183