Displaying similar documents to “Linear topological classifications of certain function spaces. II.”

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. ...

Function spaces on ordinals

Rafał Górak (2005)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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.

LΣ(≤ ω)-spaces and spaces of continuous functions

Israel Lara, Oleg Okunev (2010)

Open Mathematics

Similarity:

We present a few results and problems related to spaces of continuous functions with the topology of pointwise convergence and the classes of LΣ(≤ ω)-spaces; in particular, we prove that every Gul’ko compact space of cardinality less or equal to 𝔠 is an LΣ(≤ ω)-space.

A note on condensations of C p ( X ) onto compacta

Aleksander V. Arhangel'skii, Oleg I. Pavlov (2002)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A condensation is a one-to-one continuous mapping onto. It is shown that the space C p ( X ) of real-valued continuous functions on X in the topology of pointwise convergence very often cannot be condensed onto a compact Hausdorff space. In particular, this is so for any non-metrizable Eberlein compactum X (Theorem 19). However, there exists a non-metrizable compactum X such that C p ( X ) condenses onto a metrizable compactum (Theorem 10). Several curious open problems are formulated.

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 ) .