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
