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Inverse Limits With Set Valued Functions, Van C. Nall
Inverse Limits With Set Valued Functions, Van C. Nall
Department of Math & Statistics Faculty Publications
We begin to answer the question of which continua can be homeomorphic to an inverse limit with a single upper semi-continuous bonding map from [O, 1) to 2(O,l). Several continua including (0, 1) x (0, 1) and all compact manifolds with dimension greater than one cannot be homeomorphic to such an inverse limit. It is also shown that if the upper semi-continuous bonding maps have only zero dimensional point values, then the dimension of the inverse limit does not exceed the dimension of the factor spaces.
Locally 1-To-1 Maps And 2-To-1 Retractions, Jo Heath, Van C. Nall
Locally 1-To-1 Maps And 2-To-1 Retractions, Jo Heath, Van C. Nall
Department of Math & Statistics Faculty Publications
This paper considers the question of which continua are 2-to-1 retracts of continua.
Weak Confluence And W-Sets, Van C. Nall
Weak Confluence And W-Sets, Van C. Nall
Department of Math & Statistics Faculty Publications
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 …