Displaying similar documents to “Function spaces on ordinals”

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. ...

On the Lindelöf property of spaces of continuous functions over a Tychonoff space and its subspaces

Oleg Okunev (2009)

Commentationes Mathematicae Universitatis Carolinae

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We study relations between the Lindelöf property in the spaces of continuous functions with the topology of pointwise convergence over a Tychonoff space and over its subspaces. We prove, in particular, the following: a) if C p ( X ) is Lindelöf, Y = X ∪ { p } , and the point p has countable character in Y , then C p ( Y ) is Lindelöf; b) if Y is a cozero subspace of a Tychonoff space X , then l ( C p ( Y ) ω ) ≤ l ( C p ( X ) ω ) and ext ( C p ( Y ) ω ) ≤ ext ( C p ( X ) ω ) .

Function spaces on τ -Corson compacta and tightness of polyadic spaces

Murray G. Bell, W. Marciszewski (2004)

Czechoslovak Mathematical Journal

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We apply the general theory of τ -Corson Compact spaces to remove an unnecessary hypothesis of zero-dimensionality from a theorem on polyadic spaces of tightness τ . In particular, we prove that polyadic spaces of countable tightness are Uniform Eberlein compact spaces.