Award Date

May 2018

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Douglas Burke

Second Committee Member

Derrick DuBose

Third Committee Member

Zhonghai Ding

Fourth Committee Member

Pushkin Kachroo

Number of Pages

49

Abstract

A game tree is a nonempty set of sequences, closed under subsequences (i.e., if p ∈ T

and p extends q, then q ∈ T). If T is a game tree, then there is a natural topology on [T],

the set of paths through T. In this study we consider two types of topological spaces, both

constructed from game trees. The first is constructed by taking the Cartesian product of

two game trees, T and S: [T] × [S]. The second is constructed by the concatenation of two

game trees, T and S: [T ∗ S]. The goal of our study is to determine what conditions we

must require of the trees T and S so that these two topologies are homeomorphic.

Keywords

Canonical Function; Determinacy; Homeomorphism; Long Games; Sequence; Set Theory

Disciplines

Mathematics | Other Mathematics

Language

English


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