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Stalking the Souslin Tree—A Topological Guide

Published online by Cambridge University Press:  20 November 2018

Franklin D. Tall
Franklin D. Tall*
Affiliation:
University of Toronto
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It has long been known that the existence of a Souslin line entails (and is entailed by) the existence of a Souslin tree; indeed such a tree can be built from the open subsets of the line in a natural way. It will be shown that less onerous restrictions on a topological space than orderability allow the construction to proceed. For example, to the expected requirements-that the space satisfy the countable chain condition and not be separable, one can add the hypothesis of local connectivity, and that either first category sets be nowhere dense or that nowhere dense sets be separable.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 3 , 01 September 1976 , pp. 337 - 341
Copyright
Copyright © Canadian Mathematical Society 1976

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