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The existence of an open mapping from a compactification of a ray onto the closed unit interval [0, 1] is investigated. The main theorem says that such an open mapping does exist if and only if there is a confluent mapping of the remainder onto [0, 1].
CONTENTS1. Introduction.......................................................52. Preliminaries ....................................................83. General properties .........................................114. Mappings onto fans........................................145. Mappings onto an arc.....................................206. A characterization of the top...........................277...
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