Course - Metric Spaces MT23

Created: July 19, 2023
Updated: October 11, 2024

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Part A course that continues on from [[Course - Analysis I 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, Balls]]^U
• [[Notes - Metric Spaces MT23, Basic definitions]]^U
• [[Notes - Metric Spaces MT23, Boundedness]]^U
• [[Notes - Metric Spaces MT23, Compactness]]^U
• [[Notes - Metric Spaces MT23, Completeness]]^U
• [[Notes - Metric Spaces MT23, Connectedness]]^U
• [[Notes - Metric Spaces MT23, Contractions]]^U
• [[Notes - Metric Spaces MT23, Equivalence]]^U
• [[Notes - Metric Spaces MT23, Examples]]^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

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Related posts

• [[Notes - Metric Spaces MT23, Compactness]]^U

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• [[Course - Analysis II HT23]]^U

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• [[Notes - Complex Analysis MT23, Paths and curves]]^U

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• [[About this website]]^B

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• [[Notes - Metric Spaces MT23, Isometries]]^U

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• [[Course - Complex Analysis MT23]]^U

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• [[Notes - Metric Spaces MT23, Homeomorphisms]]^U

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• [[Courses MT23]]^U

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• [[Course - Analysis I MT22]]^U

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

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• [[University Notes]]^U

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• [[Course - Analysis III TT23]]^U

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• [[Notes - Metric Spaces MT23, Product spaces]]^U

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• [[Notes - Metric Spaces MT23, Boundedness]]^U

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

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• [[Notes - Metric Spaces MT23, Completeness]]^U

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• [[Notes - Metric Spaces MT23, Equivalence]]^U

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• [[Notes - Metric Spaces MT23, Lipschitz continuity]]^U

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• [[Notes - Metric Spaces MT23, Function spaces]]^U

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• [[Notes - Metric Spaces MT23, Limit points]]^U

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

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• [[Notes - Metric Spaces MT23, Subspaces]]^U

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• [[Notes - Metric Spaces MT23, Neighbourhoods]]^U

  (incoming)
• [[Notes - Metric Spaces MT23, Balls]]^U

  (incoming)
• [[Notes - Metric Spaces MT23, Limits and continuity]]^U

  (incoming)
• [[Notes - Metric Spaces MT23, Contractions]]^U

  (incoming)
• [[Notes - Metric Spaces MT23, Connectedness]]^U

  (incoming)
• [[Notes - Metric Spaces MT23, Basic definitions]]^U

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• [[Lecture - Metric Spaces MT23, II]]^U

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• [[Lecture - Metric Spaces MT23, IV]]^U

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