On the combinatorial principle P(c)
On the Compactness and Countable Compactness of in ZF
In the framework of ZF (Zermelo-Fraenkel set theory without the Axiom of Choice) we provide topological and Boolean-algebraic characterizations of the statements " is countably compact" and " is compact"
On the extent of star countable spaces
For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have...
On the Fréchet-Urysohn property in spaces of continuous functions
On the level spaces of fuzzy topological spaces.
On the Lindelöf property of spaces of continuous functions over a Tychonoff space and its subspaces
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 is Lindelöf, , and the point has countable character in , then is Lindelöf; b) if is a cozero subspace of a Tychonoff space , then and .
On the -fold symmetric product of a space with a --property -network (-network)
We study the relation between a space satisfying certain generalized metric properties and its -fold symmetric product satisfying the same properties. We prove that has a --property -network if and only if so does . Moreover, if is regular then has a --property -network if and only if so does . By these results, we obtain that is strict -space (strict -space) if and only if so is .
On the paracompactness of frames
Through the study of frame congruences, new characterizations of the paracompactness of frames are obtained.
On the product of a perfect paracompact space and a countable product of scattered paracompact spaces
On the shape of 0-dimensional paracompacta
On the uniform paracompactness
On the uniform paracompactness of the product of two uniform spaces
On the Whitehead theorem in shape theory I
On topologies of free groups
On total paracompactness and total metacompactness
On two classes of paracompact spaces
On unified theory for continuities.
On uniform paracompactness
On weaker forms of compactness, Lindelöfness, and countable compactness.
On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces
We introduce the concept of a family of sets generating another family. Then we prove that if X is a topological space and X has W = {W(x): x ∈ X} which is finitely generated by a countable family satisfying (F) which consists of families each Noetherian of ω-rank, then X is metaLindelöf as well as a countable product of them. We also prove that if W satisfies ω-rank (F) and, for every x ∈ X, W(x) is of the form W 0(x) ∪ W 1(x), where W 0(x) is Noetherian and W 1(x) consists of neighbourhoods of...