Identifying Open, Closed, and Compact Sets | Real Analysis Exercises

We look at six sets and determine if each one is either open, closed, compact, or any combination of the three. We will use multiple definitions in our solutions. An open set is a set whose elements all have some neighborhood around them completely contained in the set. A closed set is a complement of an open set, or equivalently a set whose limit points are all contained in the set. A compact set is closed and bounded, or equivalently a set whose open covers all have finite subcovers. #realanalysis

Thanks Summatin for the chapters!
0:00 Intro
0:20 Integers
2:07 Union of reciprocals of natural numbers with set containing zero
3:20 Real numbers
4:05 Union of open and closed intervals
5:01 Rational numbers
5:42 Singleton set containing only seven
6:23 Real numbers revisited

Open Sets:    • Intro to Open Sets (with Examples) | ...  
Closed Sets:    • All About Closed Sets and Closures of...  
Open Covers, Finite Subcovers, and Compact Sets:    • Open Covers, Finite Subcovers, and Co...  

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

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