1. The number of topological types of trees
- Author
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Krill, Thilo and Pitz, Max
- Subjects
FOS: Mathematics ,Mathematics - Combinatorics ,05C05, 05C63, 06A07 ,Mathematics - Logic ,Combinatorics (math.CO) ,Logic (math.LO) - Abstract
Two graphs are of the same topological type if they can be mutually embedded into each other topologically. We show that there are exactly $\aleph_1$ distinct topological types of countable trees. In general, for any infinite cardinal $\kappa$ there are exactly $\kappa^+$ distinct topological types of trees of size $\kappa$. This solves a problem of van der Holst from 2005., Comment: 7 pages, 1 figure
- Published
- 2023
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