Topic: Metric Spaces and Open Balls

Why Metric-Open Sets Form a Topology

Why Every Open Ball Is Open

When an Open Ball Is Not Closed

What Makes a Distance a Metric

Weighted Euclidean Metrics

Ultrametrics and the Strong Triangle Inequality

The Sup Metric and Maximum Coordinate Error

The Discrete Metric and Its Unusual Balls

Testing Candidate Sets for Metric Openness

Taxicab Distance and Coordinatewise Triangle Inequality