A Set is Closed iff it Contains Limit Points | Real Analysis

We prove the equivalence of two definitions of closed sets. We may say a set is closed if it is the complement of some open set, or a set is closed if it contains its limit points. These definitions are equivalent, so we'll prove a set is closed if and only if it contains its limit points. To do this we use contradiction for the forward direction, then to prove a set containing its limit points implies it is closed - we use the contrapositive, meaning we prove that if a set is not closed then it doesn't contain all of its limit points. #realanalysis

Open Sets:    • Intro to Open Sets (with Examples) | ...  
Closed Sets:    • All About Closed Sets and Closures of...  
Limit Points:    • Limit Points (Sequence and Neighborho...  

Real Analysis Course:    • Real Analysis  
Real Analysis exercises:    • Real Analysis Exercises  

Table of Contents
0:00 Intro


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