On Scattered Spaces

Scattered Spaces 3

Wide Scattered Spaces and Morasses

We show that it is relatively consistent with ZFC that 2ω is arbitrarily large and every sequence s = 〈sα : α < ω2〉 of infinite cardinals with sα ≤ 2ω is the cardinal sequence of some locally compact scattered space.

C-scattered fuzzy topological spaces

K e y w o r d s T o p o l o g y , C-scattered and scattered topological spaces. ('ompactness, Fuzzy perfect maps, S-paracompactness, S*-paracompactness. Fuzzy paracompactness. *-Fuzzy paracompactness. 1. I N T R O D U C T I O N The concept of C-sca t te red topological space has been defined by Telg{,rsky [1]. A space X is said to be C-sca t te red if each of its nonempty closed subspaces conta...

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

On Modal Logics Arising from Scattered Locally Compact Hausdorff Spaces

For a topological space X, let L(X) be the modal logic of X where is interpreted as interior (and hence ♦ as closure) in X. It was shown in [6] that the modal logics S4, S4.1, S4.2, S4.1.2, S4.Grz, S4.Grzn (n ≥ 1), and their intersections arise as L(X) for some Stone space X. We give an example of a scattered Stone space whose logic is not such an intersection. This gives an affirmative answer ...