Maximal Chains of Copies of the Rational Line

Abstract

We show that the class of order types of maximal chains in the partial order 〈E(ℚ)∪{∅},⊂〉, where E(ℚ) is the set of all subsets X of the rational line, ℚ, such that X with the inherited order is isomorphic to ℚ, is exactly the class of order types of compact sets of reals having the minimum non-isolated. © 2012 Springer Science+Business Media B.V.