An isomorphical classification of function spaces of zero-dimensional locally compact separable metric spaces

Jan Baars; Joost de Groot

Displaying similar documents to “An isomorphical classification of function spaces of zero-dimensional locally compact separable metric spaces”

Function spaces on ordinals

Rafał Górak (2005)

Commentationes Mathematicae Universitatis Carolinae

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We give a partial classification of spaces $C_{p} ([1, α])$ of continuous real valued functions on ordinals with the topology of pointwise convergence with respect to homeomorphisms and uniform homeomorphisms.

The Lindelöf number of C p(X)×C p(X) for strongly zero-dimensional X

Oleg Okunev (2011)

Open Mathematics

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We prove that if X is a strongly zero-dimensional space, then for every locally compact second-countable space M, C p(X, M) is a continuous image of a closed subspace of C p(X). It follows in particular, that for strongly zero-dimensional spaces X, the Lindelöf number of C p(X)×C p(X) coincides with the Lindelöf number of C p(X). We also prove that l(C p(X n)κ) ≤ l(C p(X)κ) whenever κ is an infinite cardinal and X is a strongly zero-dimensional union of at most κcompact subspaces. ...

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.