✦ LIBER ✦

Representing set-inclusion by embeddability (among the subspaces of the real line)

✍ Scribed by A.E. McCluskey; T.B.M. McMaster; W.S. Watson

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 54 KB
Volume: 96
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(98)00038-8

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✦ Synopsis

We establish that the powerset P(R) of the real line R, ordered by set-inclusion, has the same ordertype as a certain subset of P(R) ordered by homeomorphic embeddability. This is a contribution to the ongoing study of the possible ordertypes of subfamilies of P(R) under embeddability, pioneered by Banach, Kuratowski and Sierpiński.