Representing Set-inclusion by Embeddability (among the subspaces of the real line)
by
A.E. McCluskey, T.B.M. McMaster, and S.W. Watson
Proceedings of the First Summer Galway Topology Colloquium (1997)
Representing Set-inclusion by Embeddability (among the subspaces of the real line)
by
A.E. McCluskey, T.B.M. McMaster, and S.W. Watson
Proceedings of the First Summer Galway Topology Colloquium (1997)
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 Sierpinski.
partial order, ordering by homeomorphic embeddability, transfinite induction, G\delta-sets
AMS (MOS) Subject Classification: 06A06, 54H10.
This article has been published. A. E. McCluskey, T. B. M. McMaster\ and\ W. S. Watson, Representing set-inclusion by embeddability (among the subspaces of the real line). Topology Appl. {\bf 96} (1999), no.~1, 89--92; MR 2000g:54070