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Characterization of Certain Binary Relations on Connected Ordered Spaces

Published online by Cambridge University Press:  20 November 2018

James E. L'Heureux
James E. L'Heureux*
Affiliation:
University of Wisconsin
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In an earlier paper (2) reflexive transitive binary relations were considered on a connected ordered space. These relations were topologically restricted and their minimal sets were either an end point of the space or empty. It was shown that these relations could be characterized as one of the two orders of the space. Viewing the situation somewhat differently as suggested by I. S. Krule, one could say that this class of relations was characterized in terms of the identity function on the space. In this case the relations are considered in their natural setting, the product of the space with itself.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 397 - 411
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Kelley, John L., General topology (Princeton, 1955).Google Scholar
2. Krule, I. S., Concerning binary relations on connected ordered spaces, Can. J. Math., 11 (1959), 107–111.Google Scholar
3. Krule, I. S., Structs on the 1-sphere, Duke Math. J., 24 (1957), 405–414.Google Scholar
4. Strother, W. L., Continuity for multi-valued functions, Tulane University Dissertation (1952).Google Scholar
5. Wallace, A. D., Struct ideals, Proc. Amer. Math. Soc, 6 (1955), 634–638.Google Scholar