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.
 G. Hahn and J. Širáň: Three remarks on end-faithfulness
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 H. Hopf: Enden offener Raüme und unendliche diskontinuierliche Gruppen
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