On Plane Arc-smooth Structures
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.
J. J. Charatonik et al., "On Plane Arc-smooth Structures," Houston Journal of Mathematics, University of Houston, Jan 1999.
Mathematics and Statistics
Keywords and Phrases
arc-smooth; arc-structure; continuum; dendroid; hyperspace retraction; mean; plane
Article - Journal
© 1999 University of Houston, All rights reserved.