Scattered spaces II

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...

Topology Proceedings UNIVERSAL LOCALLY COMPACT SCATTERED SPACES

If δ is an ordinal, we denote by C(δ) the class of all cardinal sequences of length δ of locally compact scattered (in short: LCS) spaces. If λ is an infinite cardinal, we write Cλ(δ) = {s ∈ C(δ) : s(0) = λ = min[s(ζ) : ζ < δ]}. An LCS space X is called Cλ(δ)-universal if SEQ(X) ∈ Cλ(δ), and for each sequence s ∈ Cλ(δ) there is an open subspace Y of X with SEQ(Y ) = s. We show that • there is a...

Scattered, Hausdorff-reducible, and hereditarily irresolvable spaces

We show that a topological space is hereditarily irresolvable if and only if it is Hausdorff-reducible. We construct a compact irreducible T1-space and a connected Hausdorff space, each of which is strongly irresolvable. Furthermore, we show that the three notions of scattered, Hausdorff-reducible, and hereditarily irresolvable coincide for a large class of spaces, including metric, locally com...