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Polish Spaces and Analytic Sets
A Polish space is a separable topological space that can be metrized by means of a complete metric. A subset A of a Polish space X is analytic if there is a Polish space Z and a continuous function f : Z —> X such that f(Z)= A. After proving that each uncountable Polish space contains a non-Borel analytic subset we conclude that there exists a universally measurable non-Borel set.
Date:
August 1997
Creator:
Muller, Kimberly (Kimberly Orisja)
System:
The UNT Digital Library
A Topological Uniqueness Result for the Special Linear Groups
The goal of this paper is to establish the dependency of the topology of a simple Lie group, specifically any of the special linear groups, on its underlying group structure. The intimate relationship between a Lie group's topology and its algebraic structure dictates some necessary topological properties, such as second countability. However, the extent to which a Lie group's topology is an "algebraic phenomenon" is, to date, still not known.
Date:
August 1997
Creator:
Opalecky, Robert Vincent
System:
The UNT Digital Library