Transactions of the American Mathematical Society
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 l2, 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 K-spaces of Stadtlander. Known characterizations of smoothness in dendroids involving closed partial orders, the set function T, 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.
Citation: Pilot Scholars Version (Modified MLA Style)
Fugate, J. B.; Gordh, G. R. Jr.; and Lum, Lewis, "Arc-Smooth Continua" (1981). Mathematics Faculty Publications and Presentations. Paper 2.