# Totally disconnected not implies discrete

From Topospaces

This article gives the statement and possibly, proof, of a non-implication relation between two topological space properties. That is, it states that every topological space satisfying the first topological space property (i.e., Totally disconnected space (?)) neednotsatisfy the second topological space property (i.e., Discrete space (?))

View a complete list of topological space property non-implications | View a complete list of topological space property implications |Get help on looking up topological space property implications/non-implications

Get more facts about totally disconnected space|Get more facts about discrete space

## Statement

It is possible to have a totally disconnected space that is not a discrete space.

## Proof

### Examples

- The rational numbers, equipped with the Euclidean topology from the real line, form a totally disconnected space that is not discrete.
- The -adic numbers, equipped with the usual topology, form a compact totally disconnected space that is not discrete.