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

• Autorzy: Peter J. Nyikos
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E50: Continuum hypothesis and Martin's axiom
• 03E55: Large cardinals
• 54D30: Compactness
• 54A35: Consistency and independence results
• 54F35: Higher-dimensional local connectedness
• 54D05: Connected and locally connected spaces (general aspects)
• 03E35: Consistency and independence results
• 54D45: Local compactness, σ -compactness
• 54D15: Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 176
• Numer: 1
• Strony: 25-45

Daty

wydano

2003

Twórcy

autor

Peter J. Nyikos

• Department of Mathematics, University of South Carolina, Columbia, SC 29208, U.S.A.

Identyfikatory

DOI

10.4064/fm176-1-3