More remarks on Souslin properties and tree topologies

Pressing Down Lemma for λ-trees and its applications

“…In [8], using Lemma 2.1, K. P. Hart showed the following conclusion which is also a corollary of Corollary 2.5.…”

“…In [8], Hart showed that if T is an ω 1 -tree and T has property γ, then T is hereditarily collectionwise normal. By the proof of this result, we can get a similar result for a κ-tree.…”

“…An ω 1 -tree is a tree T such that: (1) ht(T ) = ω 1 ; (2) for each α < ω 1 , |T α | ω; (3) for every t ∈ T and for every α, ht(t) < α < ω 1 , t has at least two successors of height α; (4) if ht(t) = ht(s) is a limit ordinal, t = s if and only ift =ŝ (see [2]). In [8], Hart showed the Pressing-Down Lemma (PDL) for ω 1 -trees. Some properties of ω 1 -trees were investigated in [4] and [8].…”

“…In [8], Hart showed the Pressing-Down Lemma (PDL) for ω 1 -trees. Some properties of ω 1 -trees were investigated in [4] and [8].…”

Ortho-bases and monotonic properties

“…In [8] Hart calls a topological space X halvable if for every neighbornet U of X there exists a neighbornet V of X such that for each x, y £ X with V(x) n V(y) ^ 0 we have that x £ U(y) or y £ U(x). Clearly each monotonically normal space is halvable.…”