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Simple Links in Locally Compact Connected Hausdorff Spaces are Nondegenerate

Published online by Cambridge University Press:  20 November 2018

David John
David John*
Affiliation:
Missouri Western State College, Saint Joseph, Missouri
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The fact that simple links in locally compact connected metric spaces are nondegenerate was probably first established by C. Kuratowski and G. T. Whyburn in [2], where it is proved for Peano continua. J. L. Kelley in [3] established it for arbitrary metric continua, and A. D. Wallace extended the theorem to Hausdorff continua in [4]. In [1], B. Lehman proved this theorem for locally compact, locally connected Hausdorff spaces. We will show that the locally connected property is not necessary.

A continuum is a compact connected Hausdorff space. For any two points a and b of a connected space M, E(a, b) denotes the set of all points of M which separate a from b in M. The interval ab of M is the set E(a, b) ∪ {a, b}.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 2 , 01 April 1982 , pp. 349 - 355
Copyright
Copyright © Canadian Mathematical Society 1981

References

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