Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A characterization of locally connected continua by hyperspace retractions

Author: Sam B. Nadler
Journal: Proc. Amer. Math. Soc. 67 (1977), 167-176
MSC: Primary 54F15; Secondary 54B20
MathSciNet review: 0458378
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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".

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F15, 54B20

Retrieve articles in all journals with MSC: 54F15, 54B20

Additional Information

Keywords: Convex metric, dendrite, Hausdorff metric, hereditarily unicoherent continuum, locally connected continuum, retraction, selection
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society