Products of sequential convergence properties
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.
Products of topological spaces represent any semigroup (Preliminary communication)
Products of uniform spaces
Products of uniform spaces (Summary)
Proper shape invariants: Smoothness and calmness.
Proper shape invariants: Tameness and movability.
Properties of the covering type and a factorization theorem
Property of being semi-Kelley for the cartesian products and hyperspaces
In this paper we construct a Kelley continuum such that is not semi-Kelley, this answers a question posed by J.J. Charatonik and W.J. Charatonik in A weaker form of the property of Kelley, Topology Proc. 23 (1998), 69–99. In addition, we show that the hyperspace is not semi- Kelley. Further we show that small Whitney levels in are not semi-Kelley, answering a question posed by A. Illanes in Problemas propuestos para el taller de Teoría de continuos y sus hiperespacios, Queretaro, 2013.
Pseudo-homotopies of the pseudo-arc
Let be a continuum. Two maps are said to be pseudo-homotopic provided that there exist a continuum , points and a continuous function such that for each , and . In this paper we prove that if is the pseudo-arc, is one-to-one and is pseudo-homotopic to , then . This theorem generalizes previous results by W. Lewis and M. Sobolewski.
Pseudo-interiors of hyperspaces
Pseudoradial Spaces: Finite Products and an Example From CH
∗ The first named author’s research was partially supported by GAUK grant no. 350, partially by the Italian CNR. Both supports are gratefully acknowledged. The second author was supported by funds of Italian Ministery of University and by funds of the University of Trieste (40% and 60%).Aiming to solve some open problems concerning pseudoradial spaces, we shall present the following: Assuming CH, there are two semiradial spaces without semi-radial product. A new property of pseudoradial spaces...