Displaying similar documents to “Products of k -spaces, and questions”

Continuous selections on spaces of continuous functions

Angel Tamariz-Mascarúa (2006)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

For a space Z , we denote by ℱ ( Z ) , 𝒦 ( Z ) and ℱ 2 ( Z ) the hyperspaces of non-empty closed, compact, and subsets of cardinality ≤ 2 of Z , respectively, with their Vietoris topology. For spaces X and E , C p ( X , E ) is the space of continuous functions from X to E with its pointwise convergence topology. We analyze in this article when ℱ ( Z ) , 𝒦 ( Z ) and ℱ 2 ( Z ) have continuous selections for a space Z of the form C p ( X , E ) , where X is zero-dimensional and E is a strongly zero-dimensional metrizable space. We prove that C p ( X , E ) is weakly orderable...

Condensations of Cartesian products

Oleg I. Pavlov (1999)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We consider when one-to-one continuous mappings can improve normality-type and compactness-type properties of topological spaces. In particular, for any Tychonoff non-pseudocompact space X there is a μ such that X μ can be condensed onto a normal ( σ -compact) space if and only if there is no measurable cardinal. For any Tychonoff space X and any cardinal ν there is a Tychonoff space M which preserves many properties of X and such that any one-to-one continuous image of M μ , μ ≤ ν , contains a...

On α -normal and β -normal spaces

Aleksander V. Arhangel'skii, Lewis D. Ludwig (2001)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We define two natural normality type properties, α -normality and β -normality, and compare these notions to normality. A natural weakening of Jones Lemma immediately leads to generalizations of some important results on normal spaces. We observe that every β -normal, pseudocompact space is countably compact, and show that if X is a dense subspace of a product of metrizable spaces, then X is normal if and only if X is β -normal. All hereditarily separable spaces are α -normal. A space is...