Products of metric, uniform and topological spaces
Products of non--lower porous sets
In the present article we provide an example of two closed non--lower porous sets such that the product is lower porous. On the other hand, we prove the following: Let and be topologically complete metric spaces, let be a non--lower porous Suslin set and let be a non--porous Suslin set. Then the product is non--lower porous. We also provide a brief summary of some basic properties of lower porosity, including a simple characterization of Suslin non--lower porous sets in topologically...
Products of normal spaces with Lašnev spaces
Products of perfectly normal spaces
Products of proximites
Products of pseudoradial spaces.
Products of quotients and of -spaces
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
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.
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...
Quasi -compact spaces
Rectangular covers of products missing diagonals
We give a characterization of a paracompact -space to have a -diagonal in terms of three rectangular covers of . Moreover, we show that a local property and a global property of a space are given by the orthocompactness of .
Relative normality and product spaces
Arhangel’skiĭ defines in [Topology Appl. 70 (1996), 87–99], as one of various notions on relative topological properties, strong normality of in for a subspace of a topological space , and shows that this is equivalent to normality of , where denotes the space obtained from by making each point of isolated. In this paper we investigate for a space , its subspace and a space the normality of the product in connection with the normality of . The cases for paracompactness, more...
Remarks on Cartesian products
Remarks on cellularity in products
Remarks on chain conditions in products
Remarks on discretely absolutely star-Lindelöf spaces