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A property of hereditarily locally connected continua related to arcwise accessibility

Part of: Fairly general properties Special 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

Frolík, Z. (1960), “Concerning topological convergence of sets”, Czechoslovak Math. J. 10 (85), 168–180.CrossRefGoogle Scholar
Hocking, J. G. and Young, G. S. (1961), Topology (Addison–Wesley, Reading, Mass.).Google Scholar
Kuratowski, K. (1968), Topology II (Academic Press, New York).Google Scholar
Nishiura, T. and Tymchatyn, E. D. (1976), “Hereditarily locally connected sets”, Houston J. Math. 2, 581–596.Google Scholar
Simone, J. N. (to appear), “Concerning hereditarily locally connected continua”, Coll. Math.Google Scholar
Tymchatyn, E. D. (to appear), “Compactification of hereditarily locally connected spaces”.Google Scholar
Whyburn, G. T. (1942), Analytic Topology (Amer. Math. Soc., Providence, R.I.).CrossRefGoogle Scholar