A COMPARISON OF THE PRODUCT TOPOLOGY ON TWO TREES WITH THE TREE TOPOLOGY ON THE CONCATENATION OF TWO TREES

Cox, Katlyn K. (2022) A COMPARISON OF THE PRODUCT TOPOLOGY ON TWO TREES WITH THE TREE TOPOLOGY ON THE CONCATENATION OF TWO TREES. Doctoral thesis, UIN SAIZU Purwokerto.

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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.

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