#### Date of Defense

1968

#### Department

Mathematics

#### First Advisor

John Petro, Mathematics

#### Abstract

The basic properties of topological groups are used to prove the Fundamental Theorem of Galois Theory for arbitrary extensions and present a discussion of topological groups followed by an investigation of infinite dimensional Galois theory. Classical Galois theory is concerned with the investigation of the group of G of permutations of the roots of a polynomial equation f(x) = 0 over the field of rational numbers Q. If K is the field obtained by adjoining the roots of this polynomial to Q, then K is a finite dimensional algebraic extension of Q, and G is the group of automorphisms of K that leave each element of Q fixed.

#### Recommended Citation

Sundstrom, Theodore A., "Topological Groups and Infinite Dimensional Galois Theory" (1968). *Honors Theses*. 305.

http://scholarworks.wmich.edu/honors_theses/305

#### Access Setting

Honors Thesis-Campus Only