Abstract
AbstractInverse limits on [0, 1] with mappings cannot raise dimension. By using set-valued functions, however, such an inverse limit can be infinite dimensional. In this chapter, we examine aspects of dimension in inverse limits on [0, 1] with set-valued functions. We give an example of an inverse limit on [0, 1] with set-valued functions that has dimension 2 and another having dimension 3. We conclude this chapter with a proof that an inverse limit on [0, 1] with upper semicontinuous functions cannot be a 2-cell.KeywordsInverse LimitSemicontinuous FunctionSmall Inductive DimensionHilbert CubeFinite CollectionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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