Topological Vector Spaces 

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1.Definition: Open Ball, Neighborhood 

2.Definition: Open Set, Closed Set 

3.Definition: Clopen Set 

4.Sequences and Limits 

5.Definition: Norm, Normed Vector Space 

6.Proposition: Distance in Normed Vector Spaces 

7.Definition: Metric (Distance) 

8.Definition: Boundary Point, Boundary 

9.Definition: Continuous Functions in Metric Spaces 

10.Definition: Uniformly Continuous Functions (General Metric Spaces Case)