-spaces and -sets
Some complexity results in topology and analysis
If X is a compact metric space of dimension n, then K(X), the n- dimensional kernel of X, is the union of all n-dimensional Cantor manifolds in X. Aleksandrov raised the problem of what the descriptive complexity of K(X) could be. A straightforward analysis shows that if X is an n-dimensional complete separable metric space, then K(X) is a or PCA set. We show (a) there is an n-dimensional continuum X in for which K(X) is a complete set. In particular, ; K(X) is coanalytic but is not an analytic...
Some covering spaces and types of compactness.
Some nowhere densely generated topological properties
Some problems on Suslin spaces and topological algebras
Some questions of Arhangel'skii on rotoids
A rotoid is a space X with a special point e ∈ X and a homeomorphism F: X² → X² having F(x,x) = (x,e) and F(e,x) = (e,x) for every x ∈ X. If any point of X can be used as the point e, then X is called a strong rotoid. We study some general properties of rotoids and prove that the Sorgenfrey line is a strong rotoid, thereby answering several questions posed by A. V. Arhangel'skii, and we pose further questions.
Some relative properties on normality and paracompactness, and their absolute embeddings
Paracompactness (-paracompactness) and normality of a subspace in a space defined by Arhangel’skii and Genedi [4] are fundamental in the study of relative topological properties ([2], [3]). These notions have been investigated by primary using of the notion of weak - or weak -embeddings, which are extension properties of functions defined in [2] or [18]. In fact, Bella and Yaschenko [8] characterized Tychonoff spaces which are normal in every larger Tychonoff space, and this result is essentially...
Spaces with star countable extent
For a topological property , we say that a space is star if for every open cover of the space there exists such that . We consider space with star countable extent establishing the relations between the star countable extent property and the properties star Lindelöf and feebly Lindelöf. We describe some classes of spaces in which the star countable extent property is equivalent to either the Lindelöf property or separability. An example is given of a Tychonoff star Lindelöf space with...
Subparacompact Inverse Images of 2-subparacompact Spaces
Sum theorems for Ohio completeness
We present several sum theorems for Ohio completeness. We prove that Ohio completeness is preserved by taking σ-locally finite closed sums and also by taking point-finite open sums. We provide counterexamples to show that Ohio completeness is preserved neither by taking locally countable closed sums nor by taking countable open sums.