Nonisomorphic thin-tall superatomic Boolean algebras
Non-separable analytic spaces and measurability
Nonsupercompactness and the reduced measure algebra
Normal Vietoris implies compactness: a short proof
One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities.
Not all dyadic spaces are supercompact
Note on countable unions of Corson countably compact spaces
We show that a compact space has a dense set of points if it can be covered by countably many Corson countably compact spaces. If these Corson countably compact spaces may be chosen to be dense in , then is even Corson.
Notes on Kuratowski-Mrówka theorems in point-free context
Notion de compacité et quasi-topologie
Null-families of subsets of monotonically normal compacta
O бикoмпaктax, лeжaщиx в -пpoизвeдeнияx
On a Corson space of Todorčević
On a dense -diagonal.
On bicompacta in -products and related spaces
On bicompacta which are unions of spaces defined by means of coverings
On bicompacta which are unions of two subspaces of a certain type
On binary coproducts of frames
The structure of binary coproducts in the category of frames is analyzed, and the results are then applied widely in the study of compactness, local compactness (continuous frames), separatedness, pushouts and closed frame homomorphisms.
On certain compact topological spaces.
A compact topological space K is in the class A if it is homeomorphic to a subspace H of [0,1]I, for some set of indexes I, such that, if L is the subset of H consisting of all {xi : i C I} with xi=0 except for a countable number of i's, then L is dense in H. In this paper we show that the class A of compact spaces is not stable under continuous maps. This solves a problem posed by Deville, Godefroy and Zizler.
On -chain-net spaces.
On character and chain conditions in images of products
A scadic space is a Hausdorff continuous image of a product of compact scattered spaces. We complete a theorem begun by G. Chertanov that will establish that for each scadic space X, χ(X) = w(X). A ξ-adic space is a Hausdorff continuous image of a product of compact ordinal spaces. We introduce an either-or chain condition called Property which we show is satisfied by all ξ-adic spaces. Whereas Property is productive, we show that a weaker (but more natural) Property is not productive. Polyadic...
On compact spaces which are unions of certain collections of subspaces of special type. II.