On -embedded sets and extension of mappings
We introduce and study -embedded sets and apply them to generalize the Kuratowski Extension Theorem.
Order extension of order monomorphisms on a preordered topological space.
Ordinal remainders of classical ψ-spaces
Let ω denote the set of natural numbers. We prove: for every mod-finite ascending chain of infinite subsets of ω, there exists , an infinite maximal almost disjoint family (MADF) of infinite subsets of the natural numbers, such that the Stone-Čech remainder βψ∖ψ of the associated ψ-space, ψ = ψ(ω,ℳ ), is homeomorphic to λ + 1 with the order topology. We also prove that for every λ < ⁺, where is the tower number, there exists a mod-finite ascending chain , hence a ψ-space with Stone-Čech remainder...
Oscillations, quasi-oscillations and joint continuity.