Electronic Theses and Dissertations

The Stone-Čech Compactification and the Number of Pairwise Nonhomeomorphic Subcontinua of β[0,∞)\[0,∞)

2014-05-02

Lipham, David

thesis

Department

Mathematics and Statistics

An introduction to the Stone-Čech compactification $\beta X$ of a normal topological space $X$ is given. The method of invariantly embedding linear orders into ultrapowers is used to find $2^{\mathfrak{c}}$ pairwise nonhomeomorphic continua in $\beta\mathbb{R}$, under the assumption that the Continuum Hypothesis fails.