Course - Metric Spaces MT23

Part A course that continues on from Course - Analysis MT22^U, Course - Analysis II HT23^U and Course - Analysis III TT23^U. Those Prelim courses considered properties of the real numbers, and definitions for things like limits and continuity were given in terms of distances between real numbers. This course looks at what happens when you consider these definitions on any set that has a reasonable definition of a “distance” function (like $ \vert \cdot \vert $ for the real numbers).

• Course Webpage
• Lecture Notes
• Sister course: Course - Complex Analysis MT23^U
• Other courses this term: Courses MT23^U

Notes

• Notes - Metric Spaces MT23, Basic definitions^U

• Notes - Metric Spaces MT23, Balls^U

• Notes - Metric Spaces MT23, Boundedness^U

• Notes - Metric Spaces MT23, Examples^U

• Notes - Metric Spaces MT23, Equivalence^U

• Notes - Metric Spaces MT23, Contractions^U

• Notes - Metric Spaces MT23, Completeness^U

• Notes - Metric Spaces MT23, Connectedness^U

• Notes - Metric Spaces MT23, Compactness^U

• Notes - Metric Spaces MT23, Function spaces^U

• Notes - Metric Spaces MT23, Homeomorphisms^U

• Notes - Metric Spaces MT23, Interiors and closures^U

• Notes - Metric Spaces MT23, Isometries^U

• Notes - Metric Spaces MT23, Limit points^U

• Notes - Metric Spaces MT23, Limits and continuity^U

• Notes - Metric Spaces MT23, Lipschitz continuity^U

• Notes - Metric Spaces MT23, Neighbourhoods^U

• Notes - Metric Spaces MT23, Open and closed sets^U

• Notes - Metric Spaces MT23, Path-connectedness^U

• Notes - Metric Spaces MT23, Product spaces^U

• Notes - Metric Spaces MT23, Subspaces^U

Problem Sheets

• Sheet 1
• Sheet 2
• Sheet 3
• …carries on in Course - Complex Analysis MT23^U

Lectures

• Lecture - Metric Spaces MT23, I^U
• Lecture - Metric Spaces MT23, II^U
• Lecture - Metric Spaces MT23, III^U
• Lecture - Metric Spaces MT23, IV^U
• Lecture - Metric Spaces MT23, V^U
• Lecture - Metric Spaces MT23, VI^U
• Lecture - Metric Spaces MT23, VII^U
• Lecture - Metric Spaces MT23, VIII^U
• Lecture - Metric Spaces MT23, IX^U
• Lecture - Metric Spaces MT23, X^U
• Lecture - Metric Spaces MT23, XI^U
• Lecture - Metric Spaces MT23, XII^U