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We show that there are exactly <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\aleph _1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>\u2135<\/mml:mi>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> distinct topological types of countable trees. In general, for any infinite cardinal <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\kappa $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03ba<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> there are exactly <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\kappa ^+$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>\u03ba<\/mml:mi>\n                    <mml:mo>+<\/mml:mo>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> distinct topological types of trees of size <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\kappa $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03ba<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. This solves a problem of van der Holst from 2005.<\/jats:p>","DOI":"10.1007\/s00493-024-00087-2","type":"journal-article","created":{"date-parts":[[2024,4,4]],"date-time":"2024-04-04T12:01:41Z","timestamp":1712232101000},"page":"651-657","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Number of Topological Types of Trees"],"prefix":"10.1007","volume":"44","author":[{"given":"Thilo","family":"Krill","sequence":"first","affiliation":[]},{"given":"Max","family":"Pitz","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,4]]},"reference":[{"key":"87_CR1","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.jctb.2022.05.011","volume":"157","author":"N Bowler","year":"2022","unstructured":"Bowler, N., Elbracht, C., Erde, J., Gollin, J.P., Heuer, K., Pitz, M., Teegen, M.: Ubiquity in graphs I: topological ubiquity of trees. J. Combin. Theory Ser. 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