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Homeomorphisms of Two-Point Sets
by
Chris Good
University of Birmingham, UK
Coauthors: Ben Chad (University of Oxford)
Given a cardinal k ≤ c, a subset of the plane is said to be a k-point set if and only it it meets every line in precisely k many points.
In response to a question of Cobb, we show that for all 2 ≤ k, l < c there exists a k-point set which is homeomorphic to a l-point set.
We also show that it is consistent with ZFC that for all 2 ≤ k < c, there exists a k-point set that is homeomorphic to a l-point set for any 2 ≤ l < c, X On the other hand, we prove that is is consistent with ZFC that for all 2 ≤ k < c there exists a k-point set that is not homeomorphic to a l-point set for any distinct 2 < l ≤ c.
Date received: February 17, 2009
Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxy-79.