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Perfect GO-spaces which have a perfect linearly ordered extension

✍ Scribed by Wei-Xue Shi


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
697 KB
Volume
81
Category
Article
ISSN
0166-8641

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✦ Synopsis


It is an old problem posed by Bennett and Lutzer whether every perfect GO-space has a perfect orderable extension. As an approach to this problem, we prove that, for a perfect GO-space X, X has a perfect linearly ordered extension if and only if there is a o-discrete subset F such that GOx (0, X -F, F, 0) is perfect, where GOx (8, X -F, F, 0) is the ordered set X with the topology defined so that every point in F is isolated and every point in X -F has the usual interval neighborhood base.