A non-separable Christensen's theorem and set tri-quotient maps

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...

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.

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.

Restricted rooted non-separable planar maps

Tutte founded the theory of enumeration of planar maps in a series of papers in the 1960s. Rooted non-separable planar maps have connections, for example, to pattern-avoiding permutations, and they are in one-to-one correspondence with the β(1, 0)-trees introduced by Cori, Jacquard and Schaeffer in 1997. In this paper we enumerate 2-face-free rooted non-separable planar maps and obtain restrict...