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Souslin Properties and Tree Topologies
Author(s) -
Devlin Keith J.,
Shelah Saharon
Publication year - 1979
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-39.2.237
Subject(s) - mathematics , network topology , tree (set theory) , topology (electrical circuits) , combinatorics , computer science , computer network
Tree spaces provide a useful collection of ‘standard examples’ of topological spaces with specific properties: a fact which was already noticed by F. B. Jones in the 1930's. Certain properties of tree spaces depend upon the structural property of the tree concerned (as a partially ordered set). We obtain characterizations of those trees whose topologies are (a) normal, (b) collectionwise Hausdorff topologies. (Both results relate closely to the normal Moore space problem, and arose out of our research on that problem, the results of which appear elsewhere.) The structural properties of trees involved in these results are generalizations of the Souslin condition on trees.