A characterization of locally connected continua by hyperspace retractions

Nadler, Sam B.

doi:10.1090/S0002-9939-1977-0458378-6

A characterization of locally connected continua by hyperspace retractions
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by Sam B. Nadler

Proc. Amer. Math. Soc. 67 (1977), 167-176

DOI: https://doi.org/10.1090/S0002-9939-1977-0458378-6

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Abstract:

Let X be a (metric) continuum. It is shown that X is locally connected if and only if there is special type of retraction from ${2^X}$ onto $C(X)$, where ${2^X}$ [resp., $C(X)$] is the space of all nonempty compact subsets [resp., subcontinua] of X with the Hausdorff metric. Also, necessary and sufficient conditions are given for the “continuity of balls".

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Rétractes absolus et hyperespaces des continus

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