A detailed structure theorem is shown for locally compact, locally connected, hereditarily normal spaces and for normal, locally compact, locally connected, hereditarily ω1-scwH spaces in models of PFA(S)[S], and for the latter kinds of spaces in models of PFA. Corollaries include a powerful refinement theorem like that for monotonically normal spaces, and the corollary that the spaces involved...

Research Article Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero-Bryan and Jan van Mill S4.3 and hereditarily extremally disconnected spaces Abstract: Themodal logic S4.3 de nes the class of hereditarily extremally disconnected spaces (HED-spaces). We construct a countable HED-subspaceX of the Gleason cover of the real closed unit interval [0, 1] such that S4.3 is the logic ofX.

A Hereditarily Indecomposable asymptotic ℓ 2 Banach space is constructed. The existence of such a space answers a question of B. Maurey and verifies a conjecture of W.T. Gowers.

In this paper we examine the role of the β-space property (equivalently of the MCM-property) in generalized ordered (GO-)spaces and, more generally, in monotonically normal spaces. We show that a GO-space is metrizable iff it is a β-space with a Gδ-diagonal and iff it is a quasidevelopable β-space. That last assertion is a corollary of a general theorem that any β-space with a σ-point-finite ba...