Abstract

In general, the homotopy groups of topological spaces fail to be topological groups when endowed with the quotient topology. In this thesis, we show that for Peano continua with Abelian fundamental group, the fundamental group endowed with the quotient topology is indeed a topological group. However, this result does not extend to higher homotopy groups; that is, there exists a Peano continuum whose nth homotopy group, endowed with the quotient topology, is not a topological group. Additionally, a new characterization of the quotient topology in terms of a limit operator is introduced.

Degree

College and Department

Computational, Mathematical, and Physical Sciences; Mathematics

Rights

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