## 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)