Year: 1979
Type: article
Abstract: 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.
Authors: Keith J. Devlin, Saharon Shelah
Institutions: Lancaster University, Hebrew University of Jerusalem
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2014681471