Abstract
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.
Document Type
Article
Publication Date
2011
Publisher Statement
Copyright © 2011 Houston Journal of Mathematics. This article first appeared in Houston Journal of Mathematics 37:4 (2011), 1323-1332.
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Recommended Citation
Nall, Van C. "Inverse Limits with Set Valued Functions." Houston Journal of Mathematics 37, no. 4 (2011): 1323-1332.