Nets and compactness
Non-accessible points in extremally disconnected compact spaces I
Noncommutative Valdivia compacta
We prove some generalizations of results concerning Valdivia compact spaces (equivalently spaces with a commutative retractional skeleton) to the spaces with a retractional skeleton (not necessarily commutative). Namely, we show that the dual unit ball of a Banach space is Corson provided the dual unit ball of every equivalent norm has a retractional skeleton. Another result to be mentioned is the following. Having a compact space , we show that is Corson if and only if every continuous image...
Non-Hausdorff Ascoli theory [Book]
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