Metric Space

Links to this page
Edit this page
Entry portal
Advice For New Users

A Metric Space is a set with a concept of distance. That concept is embodied in a function which is called a metric. More formally, given a set, a metric on that set is a function d(x,y) that takes two elements and returns a real number. The metric has to satisfy the following conditions: Exercise: Using the above, prove that $d(x,y){\ge}0.$

From Metric Spaces we can get the concept of Open Sets, which in turn leads to the idea of a topological space, which manages to keep the concept of closeness, without requiring the concept of distance.

Links to this page / Page history / Last change to this page
Recent changes / Edit this page (with sufficient authority)
All pages / Search / Change password / Logout