Paracompactness and the Lindelöf property in countable products

In this paper, we prove the following: Let Y be a perfect paracompact (hereditarily Lindelöf) space and {X n: n∈ω} be a countable collection of Čech-scattered paracompact (Lindelöf) spaces, then the product Y×∏ n∈ ω X n is paracompact (Lindelöf).

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Bibliographic Details
Published in:Topology and its applications 2005, Vol.146, p.57-66
Main Authors: Aoki, Eriko, Mori, Naoko, Tanaka, Hidenori
Format: Article
Language:English
Subjects:
C-scattered
Lindelöf
Paracompact
Scattered
Čech-complete
Čech-scattered
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Description
Summary:In this paper, we prove the following: Let Y be a perfect paracompact (hereditarily Lindelöf) space and {X n: n∈ω} be a countable collection of Čech-scattered paracompact (Lindelöf) spaces, then the product Y×∏ n∈ ω X n is paracompact (Lindelöf).
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2002.12.002