Analysis · Algebra
Metric Spaces
A metric space is a set with a notion of distance. Compactness and the Banach fixed-point theorem are the main tools for proving existence and uniqueness results.
WHAT STUDENTS WILL LEARN
✓Define metric spaces; verify examples
✓Define open sets, closed sets, compactness, connectedness
✓Prove compact metric spaces are complete and totally bounded
✓Apply the Banach fixed-point theorem
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