Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4653739 | European Journal of Combinatorics | 2014 | 8 Pages |
Abstract
Countable “Urysohn metric spaces” (see the next section), with finite distance sets, are indivisible (see Sauer (2013) [19]). Countable Urysohn metric spaces are age indivisible, which follows from the Hales-Jewett theorem (Hales and Jewett (1963) [7]; see Delhommé et al. (2007) [2]). For non-Urysohn homogeneous countable metric spaces, except for the example mentioned above, the weak indivisibility question is completely open. We will show, in this paper, that a countable homogeneous ultrametric space is age indivisible if and only if it is weakly indivisible.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
N. Sauer,