On product of spaces of quasicomponents

Abstract

We use a characterization of quasicomponents by continuous functions to obtain the well known theorem which states that product of quasicomponents Q x , Q y of topological spaces X, Y, respectively, gives quasicomponent in the product space X×Y. If spaces X, Y are locally-compact, paracompact and Haussdorf, then we prove that the space of quasicomponents of the product Q(X×Y) is homeomorphic with the product space Q(X) × Q(Y), so these two spaces have the same topological properties.

Theta Omega Topological Operators and Some Product Theorems

“…In general topology, several topological properties are not finitely productive, such as paracompactness, strong paracompactness, Lindelöfness, and metacompactness. e area of research regarding the problem "What conditions on (Y, σ) and (Z, δ) to insure that their product has property P"is still hot [38][39][40][41][42][43][44][45]. e second goal of this paper is to introduce several product theorems concerning metacompactness.…”