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A property of hereditarily locally connected continua related to arcwise accessibility

Part of: Special properties Fairly general properties

Published online by Cambridge University Press:  09 April 2009

Joseph N. Simone
Joseph N. Simone
Affiliation:
University of MissouriKansas City, Missouri 64110, USA
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Abstract

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A continuum (that is, a compact connected Hausdorff space) is hereditarily locally connected if each of its subcontinua is locally connected. It is shown that a continuum X is hereditarily locally connected if and only if for each connected open set U in X and each point p in the boundary of U, U ∪ {p} is locally connected. This result is used to prove that if X is an hereditarily locally connected continuum, U is a connected open subset of X, p is an element of the boundary of U and X is first countable at p, then p is arcwise accessible from U.

MSC classification

Secondary: 54F15: Continua and generalizations 54D05: Connected and locally connected spaces (general aspects)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 1 , February 1978 , pp. 35 - 40
Copyright
Copyright © Australian Mathematical Society 1978

References

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