Subspaces of the Sorgenfrey Line

✍ Scribed by Dennis K. Burke; J.Tatch Moore

• Book ID: 104295319
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 814 KB
• Volume: 90
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(97)00181-8

✦ Synopsis

We study three problems which involve the nature of subspaces of the Sorgenfrey Line 8. It is shown that no integer power of an uncountable subspace of 9 can be embedded in a smaller power of 9. We review the known results about the existence of uncountable X & 9 where X2 is Lindel6f. These results about LindelGf powers are quite set-theoretic. A descriptive characterization is given of those subspaces of 9 which are homeomorphic to S. We show that a nonempty subspace Z c S is homeomorphic to 9 if and only if Z is dense-in-itself and is both F, and Gg in 9.