"In this dissertation we investigate zero-dimensional compact metric spaces and their inverse limits. We construct an uncountable family of zero-dimensional compact metric spaces homeomorphic to their Cartesian squares. It is known that the inverse limit on [0,1] with an upper semi-continuous function with a connected graph has either one or infinitely many points. We show that this result cannot be generalized to the inverse limits on simple triods or simple closed curves. In addition to that, we introduce a class of zero-dimensional spaces that can be obtained as the inverse limits of arcs. We complete by answering a problem by Kelly and Meddaugh about the limits of inverse limits"--Abstract, page iv.
Charatonik, W. J.
Roe, Robert Paul
Mathematics and Statistics
Ph. D. in Mathematics
Missouri University of Science and Technology
Journal article titles appearing in thesis/dissertation
- Zero-dimensional spaces homeomorphic to their Cartesian squares
- Inverse limits with bonding functions whose graphs are arcs
- Limits of inverse limits -- A counterexample
viii, 42 pages
© 2017 Sahika Sahan, All rights reserved.
Dissertation - Open Access
Electronic OCLC #
Sahan, Sahika, "Zero-dimensional spaces and their inverse limits" (2017). Doctoral Dissertations. 2749.