Topological properties of products of ordinals

被引：4
|
作者：
Kemoto, N [1 ]
Szeptycki, PJ
机构：
[1] Oita Univ, Fac Educ, Dept Math, Oita 8701192, Japan
[2] York Univ, Atkinson Fac, Toronto, ON, Canada
来源：
TOPOLOGY AND ITS APPLICATIONS | 2004年 / 143卷 / 1-3期
基金：
加拿大自然科学与工程研究理事会;
关键词：
infinite product; Sigma-product; sigma-product; elementary submodel; ordinal space; strongly zero-dimensional; countably paracompact; omega(1)-compact; normal; k-normal; quasi-perfect map;
D O I：
10.1016/j.topol.2004.06.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study separation and covering properties of special subspaces of products of ordinals. In particular, it is proven that certain subspaces of Sigma-products of ordinals are quasi-perfect preimages of Sigma-products of copies of omega. We obtain as corollaries that products of ordinals are kappa-normal and strongly zero-dimensional. Also, sigma-products and Sigma-products of ordinals are shown to be countably paracompact, kappa-normal and strongly zero-dimensional. Normality in Sigma-products and sigma-products of ordinals is also characterized. It is also shown that any continuous real-valued function on a sigma-product of ordinals has countable range. (C) 2004 Elsevier B.V. All rights reserved.
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页码：257 / 277
页数：21
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