On Plane Arc-smooth Structures

Abstract

Arc-structures on subspaces of the plane are studied in the paper. It is shown that each plane arc-smooth continuum admits an embedding in the plane such that its arc-smooth structure can be nicely extended to an arc-smooth structure on the whole plane. Using this it is proved that each plane arc-smooth continuum is a retract of the hyperspace of its closed subsets. Among several applications it is pointed out that each planar smooth dendroid admits a mean.

Department(s)

Mathematics and Statistics

Keywords and Phrases

arc-smooth; arc-structure; continuum; dendroid; hyperspace retraction; mean; plane

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1999 University of Houston, All rights reserved.

Publication Date

01 Jan 1999

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