Zero-dimensional spaces and their inverse limits

"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.

Name thesis:degree_name

Ph. D. in Mathematics

Grantor

Missouri University of Science and Technology

Author dc:creator

• Sahan, Sahika

• Mathematics

Repository record dc:identifier

https://scholarsmine.mst.edu/doctoral_dissertations/2749

OAI identifier oai:identifier

oai:scholarsmine.mst.edu:doctoral_dissertations-3754