Divisibility of countable metric spaces

Details Divisibility of countable metric spaces Divisibility of countable metric spaces

2005-10-12

arxiv.org/abs/math/0510254v1

Mathematics

Combinatorics

34 pages

Scientific paper

Prompted by a recent question of G. Hjorth as to whether a bounded Urysohn space is indivisible, that is to say has the property that any partition into finitely many pieces has one piece which contains an isometric copy of the space, we answer this question and more generally investigate partitions of countable metric spaces. We show that an indivisible metric space must be totally Cantor disconnected, which implies in particular that every Urysohn space U_V with V bounded or not but dense in some initial segment of R+, is divisible. On the other hand we also show that one can remove "large" pieces from a bounded Urysohn space with the remainder still inducing a copy of this space, providing a certain "measure" of the indivisibility. Associated with every totally Cantor disconnected space is an ultrametric space, and we go on to characterize the countable ultrametric spaces which are homogeneous and indivisible.

Affiliated with

Also associated with

No associations

Rating

Divisibility of countable metric spaces 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 Divisibility of countable metric spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Divisibility of countable metric spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-686218