We examine locally compact normal spaces in models of form PFA(S)[S], in particular characterizing paracompact, countably tight ones as those which include no perfect pre-image of ω1 and in which all separable closed subspaces are Lindelöf.

All metaLindelöf, and most countably paracompact, homogeneous manifolds are Hausdorff. Metacompact manifolds are never rigid. Every countable group can be realized as the group of autohomeomorphisms of a Lindelöf manifold. There is a rigid foliation of the plane.

Given a class $${{\mathcal {P}}}$$ of Banach spaces, locally convex space (LCS) E is called multi- if can be isomorphically embedded into product spaces that belong to . We investigate the question whether free L(X) strongly nuclear, Schwartz, multi-Hilbert or multi-reflexive. If X Tychonoff containing an infinite compact subset then, as it follows from results Außenhofer (Topol Appl 134:90–102...

We prove Sullivan's fixed-point conjecture for fixed-point-free actions of compact Lie groups which are extensions of a p-group by a torus. Moreover, we show that for a finite p-group G and a compact or finitely dimensional paracompact G-space X the fixed point set XG is nonempty iff the induced homomorphism of zero-dimensional stable cohomotopy groups 7r°(SG) -» tí0 (EG xG X) is injective. Let...

Characterizations of paracompact finite C-spaces via continuous selections avoiding Zσ-sets are given. We apply these results to obtain some properties of finite C-spaces. Factorization theorems and a completion theorem for finite C-spaces are also proved.

In this paper, we characterize stratifiable (or semi-stratifiable) spaces, and monotonically countably paracompact metacompact) spaces by expansions of locally upper bounded semi-continuous poset-valued maps. These extend earlier results for real-valued Locally functions.

For having a Poincaré duality via a cap product between the intersection homology of a paracompact oriented pseudomanifold and the cohomology given by the dual complex, G. Friedman and J. E. McClure need a coefficient field or an additional hypothesis on the torsion. In this work, by using the classical geometric process of blowing-up, adapted to a simplicial setting, we build a cochain complex...

Blind individuals manifest remarkable abilities in navigating through space despite their lack of vision. They have previously been shown to perform normally or even supra-normally in tasks involving spatial hearing in near space, a region that, however, can be calibrated with sensory-motor feedback. Here we show that blind individuals not only properly map auditory space beyond their peri-pers...