The Stone-Cech Compactification of the Plane

Abstract

The motivation for this dissertation came from Franco Obersnel's dissertation On Compactifications of the Set of Natural Numbers and the Half Line. In it he proves that any non-degenerate subcontinuum of the Stone Cech remainder of the half line will map onto any arbitrary continuum of weight ≤ ω₁. We are able to prove the same property for many (though not all) non-degenerate subcontinua of the Stone-Cech remainder of the plane, as well as investigating certain algebraic and topological structures on subsets of the remainder.