Access Type

Open Access Dissertation

Date of Award


Degree Type


Degree Name




First Advisor

Daniel C. Isaksen


Topology has recently received more attention from statisticians as some its tools have been applied to understanding the shape of data. In particular, a data set can generate a topological space, and this space’s topological structure can give us insight into some properties of the data. This framework has made it necessary to study random spaces generated by data. For example, without an understanding of the probabilistic properties of random spaces, one cannot conclude with any degree of confidence what the tools of topology tell us about a data set. While some results are known about the cohomological structure of a random space, not much is known about how cohomology operations behave on random spaces. This dissertation proves some results about the asymptotic properties of cohomology operations on random spaces and discusses the idea of a random Bockstein operation in a related purely algebraic context.