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On Disjoint Connected Subsets of a Square Containing Pairs of Antipodal Points

Published online by Cambridge University Press:  20 November 2018

D. Morrison ,
M. Kiang  and
J. Wright
D. Morrison
Affiliation:
Dalhousie University, Halifax
M. Kiang
Affiliation:
Dalhousie University, Halifax
J. Wright
Affiliation:
Dalhousie University, Halifax
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In [1], p. 132, it is shown that there exist two disjoint subsets of a square each connecting a pair of opposite vertices. Our interest in obtaining covers by infinite collections of such sets was prompted by a question posed by R.B. Reed in [3], We are grateful also to Dr. M. Edelstein for his guidance and encouragement of our work on the subject.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 5 , December 1966 , pp. 631 - 638
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Gelbaum, B. R. and Olmstead, J.M.H., Counter-examples in analysis. Holden-Day, San Francisco (1964).Google Scholar
2. Newman, M. H. A., Elements of the topology of plane sets of points. 2nd. ed. Univer sity Press, Cambridge (1951).Google Scholar
3. Reed, R.B., Problem P 108, Canadian Mathematical Bulletin, 8 (1965), page 837.Google Scholar
4. Whyburn, G. T., Analytic topology. Amer. Math. Soc, Colloquium publications, XXVIII (1942). Amer. Math. Soc., New York City.Google Scholar