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Totally disconnected not implies discrete

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 (?)) need not satisfy the second topological space property (i.e., Discrete space (?))
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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 p-adic numbers, equipped with the usual topology, form a compact totally disconnected space that is not discrete.