Title

Arc Approximation Property and Confluence of Induced Mappings

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.

Department(s)

Mathematics and Statistics

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1998 Rocky Mountain Mathematics Consortium, All rights reserved.


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