Tri-quotient maps are preserved by infinite products

Generalized tri-quotient maps and Čech-completeness

For a topological space X let K(X) be the set of all compact subsets of X. The purpose of this paper is to characterize Lindelöf Čech-complete spaces X by means of the sets K(X). Similar characterizations also hold for Lindelöf locally compact X, as well as for countably K-determined spaces X. Our results extend a classical result of J. Christensen.

A Non-separable Christensen’s Theorem and Set Tri-quotient Maps

For every space X let K(X) be the set of all compact subsets of X . Christensen [6] proved that if X, Y are separable metrizable spaces and F : K(X) → K(Y ) is a monotone map such that any L ∈ K(Y ) is covered by F (K) for some K ∈ K(X), then Y is complete provided X is complete. It is well known [3] that this result is not true for non-separable spaces. In this paper we discuss some additional...

Relative Compactness and Product Stable Quotient Maps

Regularity of Bounded Tri-Linear Maps and the Fourth Adjoint of a Tri-Derivation

In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if f : X × Y × Z −→ W is a bounded tri-linear mapping and h : W −→ S is a bounded linear mapping, then f is regular if and only if hof is regular. We also shall give some necessary and sufficient conditions such that the fourth adjoint D^∗∗∗∗ of a tri-derivation D is again tri-derivation.

Infinite Products of Infinite Measures

Let (Xi, Bi, mi) (i ∈ N) be a sequence of Borel measure spaces. There is a Borel measure μ on ∏ i∈N Xi such that if Ki ⊆ Xi is compact for all i ∈ N and ∏ i∈N mi(Ki) converges then μ( ∏ i∈N Ki) = ∏ i∈N mi(Ki)