Open and proper maps between convergence spaces
Open maps do not preserve Whyburn property
We show that a (weakly) Whyburn space may be mapped continuously via an open map onto a non (weakly) Whyburn space . This fact may happen even between topological groups and , a homomorphism, Whyburn and not even weakly Whyburn.
Order compatibility for Cauchy spaces and convergence spaces.
Ordered Cauchy spaces.
Oб одной задаче Э. Чеха
-regular Cauchy completions.
-topological and -regular: Dual notions in convergence theory.
Pointwise convergence fails to be strict
It is known that the ring of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of . In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of which differs from .
Pontryagin duality for convergence groups of unimodular continuous functions
Preconvergence compactness and p-closed spaces.
Probabilistic approach spaces
We study a probabilistic generalization of Lowen's approach spaces. Such a probabilistic approach space is defined in terms of a probabilistic distance which assigns to a point and a subset a distance distribution function. We give a suitable axiom scheme and show that the resulting category is isomorphic to the category of left-continuous probabilistic topological convergence spaces and hence is a topological category. We further show that the category of Lowen's approach spaces is isomorphic to...
Probabilistic convergence spaces and generalized metric spaces.
Probabilistic convergence spaces and regularity.
Probabilistic convergence structures.
Probabilistic Topologies Induced by L-Fuzzy Uniformities.
Productively Fréchet spaces
We solve the long standing problem of characterizing the class of strongly Fréchet spaces whose product with every strongly Fréchet space is also Fréchet.
Products of coarse convergence groups
Products of convergence properties
Products of pseudoradial spaces.
Products of topological spaces and families of filters
We show that, under suitably general formulations, covering properties, accumulation properties and filter convergence are all equivalent notions. This general correspondence is exemplified in the study of products. We prove that a product is Lindelöf if and only if all subproducts by factors are Lindelöf. Parallel results are obtained for final -compactness, -compactness, the Menger and the Rothberger properties.