Tree-Like Spaces with the Fixed-Point Property, Realized as Inverse Limits of Special Finite Trees

Author

Jennifer Katherine Aust, University of Tennessee - Knoxville

Date of Award

12-2008

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Robert J. Daverman

Committee Members

Morwen Thistlethwaite, Pavlos Tzermias

Abstract

In this paper, we explore some properties of inverse limit sequences on sub-spaces of Euclidean n-space. We address some well-known examples, in particular the example by David Bellamy of the "tree-like" continuum that does not have the fixed-point property. We highlight some spaces with the fixed-point property that are between snake-like continua and Bellamy's example in their level of complexity. Specifically, we prove the fixed-point property for inverse limits of limit sequences on the unit interval and on the n-ad (in two configurations), and for inverse limits that can be mapped via a continuous function with small point pre-images to a generalized relative of the n-ad, which we call the (m, n)-ad. We conclude with a sufficient condition on a tree-like space for the space to have the fixed-point property.

Recommended Citation

Aust, Jennifer Katherine, "Tree-Like Spaces with the Fixed-Point Property, Realized as Inverse Limits of Special Finite Trees. " Master's Thesis, University of Tennessee, 2008.
https://trace.tennessee.edu/utk_gradthes/3637