Introduction to Metric Spaces
Definition
Examples
Example 1: with Euclidean metric:
Example 2: with taxicab metric:
Example 3: with supremum metric:
Example 4: with
Example 5: Discrete metric: if , if
Open Balls
Topology from Metric
Convergence
Cauchy Sequences
Isometry
Isometric spaces are essentially the same (identical metric structure).
Bounded Sets
Diameter
Lipschitz Maps
Examples of Metric Spaces
Product Metrics
These generate the product topology.