Products of hereditarily indecomposable continua are 2-connected
Products of -spaces, and questions
As is well-known, every product of a locally compact space with a -space is a -space. But, the product of a separable metric space with a -space need not be a -space. In this paper, we consider conditions for products to be -spaces, and pose some related questions.
Products of Lindelöf -spaces are Lindelöf – in some models of ZF
The stability of the Lindelöf property under the formation of products and of sums is investigated in ZF (= Zermelo-Fraenkel set theory without AC, the axiom of choice). It is • not surprising that countable summability of the Lindelöf property requires some weak choice principle, • highly surprising, however, that productivity of the Lindelöf property is guaranteed by a drastic failure of AC, • amusing that finite summability of the Lindelöf property takes place if either some weak choice principle...
Products of locally connected locales
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...