The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

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

Similarity:

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

Similarity:

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 ) .