Images of the Cantor Fan

Author

J. J. Charatonik
W. J. Charatonik, Missouri University of Science and TechnologyFollow

Abstract

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.

Recommended Citation

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 https://doi.org/10.1016/S0166-8641(89)80005-7

Department(s)

Mathematics and Statistics

Keywords and Phrases

image; light; open; arc; fan; end point; monotone; dendroid; retract; smooth; property of Kelley; Cantor fan; continuous; confluent

International Standard Serial Number (ISSN)

0166-8641

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1989 Elsevier, All rights reserved.

Publication Date

01 Jan 1989