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Cyclic Element Theory in Connected and Locally Connected Hausdorff Spaces

Published online by Cambridge University Press:  20 November 2018

B. Lehman
B. Lehman*
Affiliation:
University of Guelph, Guelph, Ontario
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G. T. Whyburn, in 1926, began the development of cyclic element theory for Peano continua. This theory proved fruitful in the study of Peano spaces and a comprehensive development of the theory for metric spaces was presented in [6]. An excellent history of the theory is to be found in [4]. In [7] and [5] the generalization of cyclic element theory to more general spaces was begun. However, in each of these papers only basic definitions were set forth and fundamental results obtained. In this paper, we concern ourselves primarily with connected and locally connected Hausdorff spaces, developing the cyclic element theory initiated in [7] and demonstrating that the theory has many of the applications to connected and locally connected Hausdorff spaces that the classical theory has to Peano spaces.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 5 , 01 October 1976 , pp. 1032 - 1050
Copyright
Copyright © Canadian Mathematical Society 1976

References

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