Master of Science (MS)
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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.
Canonical Function; Determinacy; Homeomorphism; Long Games; Sequence; Set Theory
Mathematics | Other Mathematics
Cox, Katlyn Kathleen, "A Comparison of the Product Topology on Two Trees with the Tree Topology on the Concatenation of Two Trees" (2018). UNLV Theses, Dissertations, Professional Papers, and Capstones. 3236.