Countable paracompactness versus normality in ω21

✍ Scribed by Nobuyuki Kemoto; Kerry D. Smith; Paul J. Szeptycki

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 125 KB
• Volume: 104
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00023-1

✦ Synopsis

We will see that:

(1) In ZFC, for each subspace X ⊆ ω 2 1 , the following are equivalent; (a) X is normal, (b) X is countably paracompact and strongly collectionwise Hausdorff, (c) X is expandable.

(2) Under a variety of different set-theoretic assumptions (including V = L and PMEA) all countably paracompact subspaces of ω 2 1 are normal.

(3) All subspaces of ω 2 1 are collectionwise Hausdorff.