✦ LIBER ✦
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
No coin nor oath required. For personal study only.
✦ 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.