10 Metric spaces[0MR]
10.1 Definitions
10.2 Topology in metric spaces
10.3 Quotients
10.4 Distance function
10.5 Connected set
10.6 Topology in the real line
10.7 Topology in Euclidean spaces
10.8 Fixed points
10.9 Isometries
10.10 Compactness
10.11 Baire’s Theorem and categories
The following is Baire’s category theorem; there are several equivalent statements.
Theorem
3
Definition
4
The Cantor set is a perfect set, see [09S].
10.12 Infinite product of metric spaces
10.13 Ultrametric
[ [0WK]]
Definition
5
[ [0WZ]]
Ultrametric space of sequences
Let’s build this example of ultrametric on the space of sequences.
Definition
6
Remark
7
See also [0ZP].