✦ LIBER ✦

Generalized paracompactness of subspaces in products of two ordinals

✍ Scribed by Nobuyuki Kemoto; Ken-ichi Tamano; Yukinobu Yajima

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 118 KB
Volume: 104
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(99)00010-3

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✦ Synopsis

We will characterize metacompactness, subparacompactness and paracompactness of subspaces of products of two ordinal numbers. Using them we will show:

(1) For such subspaces, weak submetaLindelöfness, screenability and metacompactness are equivalent.

(2) Metacompact subspaces of ω 2 1 are paracompact. (3) Metacompact subspaces of ω 2 2 are subparacompact. (4) There is a metacompact subspace of (ω 1 + 1) 2 which is not paracompact.

(5) There is a metacompact subspace of (ω 2 + 1) 2 which is not subparacompact.

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