Arc Approximation Property and Confluence of Induced Mappings

Author

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

Abstract

We say that a continuum X has the arc approximation property if every subcontinuum K of X is the limit of a sequence of arcwise connected subcontinua of X all containing a fixed point of K. This property is applied to exhibit a class of continua Y such that confluence of a mapping f : X - Y implies confluence of the induced mappings 2^f : 2^x - @^y and C(f) : C(x) - C(y). The converse implications are studied and similar interrelations are considered for some other classes of mappings, related to confluent ones.

Recommended Citation

W. J. Charatonik, "Arc Approximation Property and Confluence of Induced Mappings," Rocky Mountain Journal of Mathematics, Rocky Mountain Mathematics Consortium, Jan 1998.

The definitive version is available at https://doi.org/10.1216/rmjm/1181071825

Department(s)

Mathematics and Statistics

International Standard Serial Number (ISSN)

0035-7596

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 1998 Rocky Mountain Mathematics Consortium, All rights reserved.

Publication Date

01 Jan 1998