Metric spaces
Definition.
Let be a set. A function
is called a metric if it satisfies the following three
conditions:
1.
(positive definitness)
2.
3.
A pair
, where is a metric on is called a metric space.
Examples.
0. Any set
with
- discrete metric.
1.
w

Chapter 1
Metric Spaces
Many of the arguments you have seen in several variable calculus are almost
identical to the corresponding arguments in one variable calculus, especially
arguments concerning convergence and continuity. The reason is that the
notio

Metric and Topological Spaces
T. W. Korner
August 17, 2015
Small print The syllabus for the course is defined by the Faculty Board Schedules
(which are minimal for lecturing and maximal for examining). What is presented here
contains some results which it