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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

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✦ 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.


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