Projects and Assignments in Pure Mathematics
Topological Groups
This project requires some familiarity with the Topology course, and so is
probably only suitable at 4MM level. A
topological group, as you might have suspected, is a group with a
topology
on it, satisfying certain natural axioms. The most familiar examples
are
the integers, the reals and the unit circle in the complex plane (under
multiplication), and we can study "harmonic analysis" in this, and
other
contexts. The most comprehensive book is Hewitt and Ross, "Abstract
Harmonic Analysis", but you can also find easier introductions to the
subject.
Books
Hewitt and Ross, Abstract
Harmonic Analysis, Springer, 1963.
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