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.
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
Mathematics and Statistics
International Standard Serial Number (ISSN)
Article - Journal
© 1998 Rocky Mountain Mathematics Consortium, All rights reserved.
01 Jan 1998