Arcs in the Plane

Details Arcs in the Plane Arcs in the Plane

2009-06-15

arxiv.org/abs/0906.2753v1

Mathematics

General Topology

14 pages

Scientific paper

Assuming PFA, every uncountable subset E of the plane meets some C^1 arc in
an uncountable set. This is not provable from MA(aleph_1), although in the case
that E is analytic, this is a ZFC result. The result is false in ZFC for C^2
arcs, and the counter-example is a perfect set.

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