Article
Summary:
We prove that a countable connected graph has an end-faithful spanning tree that contains a prescribed set of rays whenever this set is countable, and we show that this solution is, in a certain sense, the best possible. This improves a result of Hahn and Širáň Theorem 1.
References:
[2] G. Hahn and J. Širáň:
Three remarks on end-faithfulness. Finite and Infinite Combinatorics in Sets and Logic, N. Sauer et al. (eds.), Kluwer, 1993, pp. 125–133.
MR 1261200
[4] H. Hopf:
Enden offener Raüme und unendliche diskontinuierliche Gruppen. Comm. Math. Helv. 15 (1943), 27–32.
MR 0007646