Arc-smooth continua
Authors:
J. B. Fugate, G. R. Gordh and Lewis Lum
Journal:
Trans. Amer. Math. Soc. 265 (1981), 545-561
MSC:
Primary 54F20; Secondary 54F50
DOI:
https://doi.org/10.1090/S0002-9947-1981-0610965-3
MathSciNet review:
610965
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Abstract | References | Similar Articles | Additional Information
Abstract: Continua admitting arc-structures and arc-smooth continua are introduced as higher dimensional analogues of dendroids and smooth dendroids, respectively. These continua include such spaces as: cones over compacta, convex continua in , strongly convex metric continua, injectively metrizable continua, as well as various topological semigroups, partially ordered spaces, and hyperspaces. The arc-smooth continua are shown to coincide with the freely contractible continua and with the metric
-spaces of Stadtlander. Known characterizations of smoothness in dendroids involving closed partial orders, the set function
, radially convex metrics, continuous selections, and order preserving mappings are extended to the setting of continua with arc-structures. Various consequences of the special contractibility properties of arc-smooth continua are also obtained.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1981-0610965-3
Keywords:
Continuous selection,
contractibility,
convex metric,
dendrite,
dendroid,
fixed point set,
hyperspace of subcontinua,
order preserving mapping,
partially ordered space,
set function ,
smooth continuum,
smooth dendroid,
thread action,
topological semigroup
Article copyright:
© Copyright 1981
American Mathematical Society