Weak confluence and W-sets

Date

1983

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Abstract

If K is a subcontinuum of a continuum M such that K is contained in every continuum in M which intersects K and its complement, then K is called a C-set. It has been observed that every map from a continuum onto M is confluent with respect to a C-set. That is, for every map of a continuum onto M every component of the preimage of a C-set K maps onto K. A map of a continuum onto M is said to be weakly confluent with respect to a subcontinuum K if some component of the preimage of K maps onto K. If K is a subcontinuum of M such that every map of a continuum onto M is weakly confluent with respect to K, then K will be called a W-set. In this paper some fundamental properties of W-sets are discussed, and characterizations of W-sets in atriodic continua are given.

Description

Keywords

C*-algebras

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