Images of the Cantor Fan
Structural characterizations are obtained of images of the Cantor fan (i.e., the cone over the Cantor set) under mappings that belong to one of the following classes: confluent, open, monotone, retractions, light, and any intersections of these. A necessary and sufficient condition is shown under which there exists a monotone mapping from an arbitrary fan onto an arc.
J. J. Charatonik and W. J. Charatonik, "Images of the Cantor Fan," Topology and its Applications, Elsevier, Jan 1989.
The definitive version is available at http://dx.doi.org/10.1016/S0166-8641(89)80005-7
Mathematics and Statistics
Keywords and Phrases
image; light; open; arc; fan; end point; monotone; dendroid; retract; smooth; property of Kelley; Cantor fan; continuous; confluent
Article - Journal
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