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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Intervals of continua which are Hilbert cubes


Author: Carl Eberhart
Journal: Proc. Amer. Math. Soc. 68 (1978), 220-224
MSC: Primary 54F15; Secondary 57N20
MathSciNet review: 480197
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Abstract: If P is a subcontinuum of a metric continuum X, then by the interval of continua $ \mathcal{C}(P,X)$ we mean the space of all subcontinua of X which contain P (with the Hausdorff metric). We show that $ \mathcal{C}(P,X)$ is often homeomorphic with the Hilbert cube.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0480197-6
PII: S 0002-9939(1978)0480197-6
Keywords: Interval of continua, annular pair, cover
Article copyright: © Copyright 1978 American Mathematical Society