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Hyperspace retractions for curves

AbstractWe study retractions from the hyperspace of all nonempty closed subsets of a given continuum onto the continuum (which is naturally embedded in the hyperspace). Some necessary and some sufficient conditions for the existence of such a retraction are found if the continuum is a curve. It is shown that the existence of such a retraction for a curve implies that the curve is a uniformly arcwise connected dendroid, and that a universal smooth dendroid admits such a retraction. The existence...

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