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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.

Information

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

References

1. Aarts, J. M. and Lutzer, D. J., Completeness properties designed for recognizing Baire spaces, Dissert. Math. 16 (1974), 1–48.Google Scholar
2. Amirdzanov, G. P. and Šapirovskiĭ, B. E., On everywhere dense subsets of topological spaces, Soviet Math. Dokl. 15 (1974), 87–92.Google Scholar
3. Creede, G., Semistratifiable spaces, 318–323 in: Topology Conference, Arizona State University, 1967, Tempe, 1968.Google Scholar
4. Devlin, K. and Jöhnsbraten, H., The Souslin Problem, Lect. Notes. Math. 405 (Springer-Verlag, Berlin).Google Scholar
5. Goffman, C. and Waterman, D., Approximately continuous transformations, Proc. Amer. Math. Soc. 12 (1961), 116–121.Google Scholar
6. Kelley, J. L., Measures on boolean algebras, Pacific J. Math. 9 (1959), 1165–1177.Google Scholar
7. Kurepa, G., La condition de Suslin et une propriété caractéristique des nombres réels, C.R. Acad. Sci. Paris 231 (1950), 1113–1114.Google Scholar
8. Pixley, C. and Roy, P., Uncompletable Moore spaces, 75–85 in: Proceedings of the Auburn topology conference, March, 1969, Auburn, Alabama, 1969.Google Scholar
9. Rudin, M. E. (Estill), Separation in non-separable spaces, Duke Math. J. 18 (1951), 623–629.Google Scholar
10. Rudin, M. E. (Estill), Concerning a problem of Souslin’s, Duke Math. J. 19 (1952), 629–640.Google Scholar
11. Rudin, M. E., Souslin’s conjecture, Amer. Math. Monthly 76 (1969), 1113–1119.Google Scholar
12. Tall, F. D., On the existence of non-metrizable hereditarily Lindelöf spaces with pointcountable bases, Duke Math. J. 41 (1974), 299–304.Google Scholar
13. Tall, F. D., The density topology, Pacific J. Math., 62 (1976), 275–284.Google Scholar