On minimal non-potentially closed subsets of the plane

Details On minimal non-potentially closed subsets of the plane On minimal non-potentially closed subsets of the plane

2007-09-30

arxiv.org/abs/0710.0152v1

Topology and its Applications 154, 1 (2007) 241-262

Mathematics

Logic

Scientific paper

We study the Borel subsets of the plane that can be made closed by refining the Polish topology on the real line. These sets are called potentially closed. We first compare Borel subsets of the plane using products of continuous functions. We show the existence of a perfect antichain made of minimal sets among non-potentially closed sets. We apply this result to graphs, quasi-orders and partial orders. We also give a non-potentially closed set minimum for another notion of comparison. Finally, we show that we cannot have injectivity in the Kechris-Solecki-Todorcevic dichotomy about analytic graphs.

Affiliated with

Also associated with

No associations

Rating

On minimal non-potentially closed subsets of the plane does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On minimal non-potentially closed subsets of the plane, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On minimal non-potentially closed subsets of the plane will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-721839