Displaying similar documents to “Transfinite inductions producing coanalytic sets”

M-bases in spaces of continuous functions on ordinals

Ondrej F. K. Kalenda (2002)

Colloquium Mathematicae

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We prove, among other things, that the space C[0,ω₂] has no countably norming Markushevich basis. This answers a question asked by G. Alexandrov and A. Plichko.

First countable spaces without point-countable π-bases

István Juhász, Lajos Soukup, Zoltán Szentmiklóssy (2007)

Fundamenta Mathematicae

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We answer several questions of V. Tkachuk [Fund. Math. 186 (2005)] by showing that ∙ there is a ZFC example of a first countable, 0-dimensional Hausdorff space with no point-countable π-base (in fact, the minimum order of a π-base of the space can be made arbitrarily large); ∙ if there is a κ-Suslin line then there is a first countable GO-space of cardinality κ⁺ in which the order of any π-base is at least κ; ∙ it is consistent to have a...

Dimension of countable intersections of some sets arising in expansions in non-integer bases

David Färm, Tomas Persson, Jörg Schmeling (2010)

Fundamenta Mathematicae

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We consider expansions of real numbers in non-integer bases. These expansions are generated by β-shifts. We prove that some sets arising in metric number theory have the countable intersection property. This allows us to consider sets of reals that have common properties in a countable number of different (non-integer) bases. Some of the results are new even for integer bases.

Definability of small puncture sets

Andrés Eduardo Caicedo, John Daniel Clemens, Clinton Taylor Conley, Benjamin David Miller (2011)

Fundamenta Mathematicae

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We characterize the class of definable families of countable sets for which there is a single countable definable set intersecting every element of the family.

On n -in-countable bases

S. A. Peregudov (2000)

Commentationes Mathematicae Universitatis Carolinae

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Some results concerning spaces with countably weakly uniform bases are generalized for spaces with n -in-countable ones.

Spaces of continuous characteristic functions

Raushan Z. Buzyakova (2006)

Commentationes Mathematicae Universitatis Carolinae

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We show that if X is first-countable, of countable extent, and a subspace of some ordinal, then C p ( X , 2 ) is Lindelöf.