Weak Confluence and W-Sets

A mapping between continua is weakly confluent if for each subcontinuum K of the range some component of the preimage of K maps onto K. Class [W] is the class of all continua which are the images of weakly confluent maps only. The notion of Class [W] was introduced by Andrej Lelek in 1972. Since then it has been widely explored and some characterizations of these continua have been given. J. Grispolakis and E. D. Tymchatyn have given a characterization in terms of hyperspaces [4]. J. Davis has shown that acyclic atriodic continua are in Class [W]i therefore, atriodic tree-like continua are in Class [W] [2]. G. Feuerbacher has shown that non chainable circle-like continua are in Class [W] if and only if they are not weakly chainable [3, Thm. 7, p. 21]. Here a new approach is taken, and some further results about atriodic continua and Class [W] are obtained