Applications of some strong set-theoretic axioms to locally compact T₅ and hereditarily scwH spaces

Peter J. Nyikos. "Applications of some strong set-theoretic axioms to locally compact T₅ and hereditarily scwH spaces." Fundamenta Mathematicae 176.1 (2003): 25-45. <http://eudml.org/doc/282789>.

@article{PeterJ2003,
abstract = {Under some very strong set-theoretic hypotheses, hereditarily normal spaces (also referred to as T₅ spaces) that are locally compact and hereditarily collectionwise Hausdorff can have a highly simplified structure. This paper gives a structure theorem (Theorem 1) that applies to all such ω₁-compact spaces and another (Theorem 4) to all such spaces of Lindelöf number ≤ ℵ₁. It also introduces an axiom (Axiom F) on crowding of functions, with consequences (Theorem 3) for the crowding of countably compact subspaces in certain continuous preimages of ω₁. It also exposes (Theorem 2) the fine structure of perfect preimages of ω₁ which are T₅ and hereditarily collectionwise Hausdorff. In these theorems, "T₅ and hereditarily collectionwise Hausdorff" is weakened to "hereditarily strongly collectionwise Hausdorff." Corollaries include the consistency, modulo large cardinals, of every hereditarily strongly collectionwise Hausdorff manifold of dimension > 1 being metrizable. The concept of an alignment plays an important role in formulating several of the structure theorems.},
author = {Peter J. Nyikos},
journal = {Fundamenta Mathematicae},
keywords = {locally compact; hereditarily cwH; countably compact; hereditarily normal; copies of },
language = {eng},
number = {1},
pages = {25-45},
title = {Applications of some strong set-theoretic axioms to locally compact T₅ and hereditarily scwH spaces},
url = {http://eudml.org/doc/282789},
volume = {176},
year = {2003},
}

TY - JOUR
AU - Peter J. Nyikos
TI - Applications of some strong set-theoretic axioms to locally compact T₅ and hereditarily scwH spaces
JO - Fundamenta Mathematicae
PY - 2003
VL - 176
IS - 1
SP - 25
EP - 45
AB - Under some very strong set-theoretic hypotheses, hereditarily normal spaces (also referred to as T₅ spaces) that are locally compact and hereditarily collectionwise Hausdorff can have a highly simplified structure. This paper gives a structure theorem (Theorem 1) that applies to all such ω₁-compact spaces and another (Theorem 4) to all such spaces of Lindelöf number ≤ ℵ₁. It also introduces an axiom (Axiom F) on crowding of functions, with consequences (Theorem 3) for the crowding of countably compact subspaces in certain continuous preimages of ω₁. It also exposes (Theorem 2) the fine structure of perfect preimages of ω₁ which are T₅ and hereditarily collectionwise Hausdorff. In these theorems, "T₅ and hereditarily collectionwise Hausdorff" is weakened to "hereditarily strongly collectionwise Hausdorff." Corollaries include the consistency, modulo large cardinals, of every hereditarily strongly collectionwise Hausdorff manifold of dimension > 1 being metrizable. The concept of an alignment plays an important role in formulating several of the structure theorems.
LA - eng
KW - locally compact; hereditarily cwH; countably compact; hereditarily normal; copies of
UR - http://eudml.org/doc/282789
ER -