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Date of Award
Restricted Thesis: Campus only access
Bachelor of Science
Dr. Van Nall
Recent work on inverse limits has led to increased interest in questions such as: given a topological space X, is there an inverse sequence such that the inverse limit on that inverse sequence is X. Work done with inverse limits on continuous functions have shown that the inverse limit is always at most 1-dimensional, which has led to an interest in constructing inverse sequence with upper-semi continuous set-valued functions whose inverse limits are more than 1-dimensional In this thesis, we show a construction that raises the dimension of the inverse limit. This same construction shows that it is possible to have [0, 1]k embedded in an inverse limit. We mention a recent result that it is not possible to have the inverse limit with a single bonding map be homeomorphic to [0, 1]k. Finally, we conclude with a few illustrative examples.
Torkornoo, Desmond, "Constructing [0,1]k in the inverse limit on [0,1]" (2008). Honors Theses. 674.