A compact Fréchet space whose square is not Fréchet
A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube
We compare the forcing-related properties of a complete Boolean algebra with the properties of the convergences (the algebraic convergence) and on generalizing the convergence on the Cantor and Aleksandrov cube, respectively. In particular, we show that is a topological convergence iff forcing by does not produce new reals and that is weakly topological if satisfies condition (implied by the -cc). On the other hand, if is a weakly topological convergence, then is a -cc algebra...
A Generalization of Chain-net Spaces
A hedgehog in a product
A large -discrete Fréchet space having the Souslin property
A non-Skorokhod topology on the Skorokhod space.
A note on diagonal and matrix properties of convergence spaces
A note on Fréchet spaces
A note on -metrizable spaces
In this paper, the relationships between metric spaces and -metrizable spaces are established in terms of certain quotient mappings, which is an answer to Alexandroff’s problems.
A note on products of Fréchet spaces
A note on sequence-covering -images of metric spaces
A note on transfinite sequences
A sequential analogue of the Grothendieck-Pták topology
A tiny peculiar Fréchet space
A weakly pseudocompact subspace of Banach space is weakly compact
Absolute countable compactness of products and topological groups
In this paper, we generalize Vaughan's and Bonanzinga's results on absolute countable compactness of product spaces and give an example of a separable, countably compact, topological group which is not absolutely countably compact. The example answers questions of Matveev [8, Question 1] and Vaughan [9, Question (1)].
Accessibility spaces, -spaces and initial topologies
Almost closed sets and topologies they determine
We prove that every countably compact AP-space is Fréchet-Urysohn. It is also established that if is a paracompact space and is AP, then is a Hurewicz space. We show that every scattered space is WAP and give an example of a hereditarily WAP-space which is not an AP-space.
An Ascoli theorem for sequential spaces.