Continuity of the identity function

Task number: 3169

Let \((X,\rho)\) be a metric space. Show that the identity function \(\operatorname{id} \colon X \to X\) defined as \(\operatorname{id}(x) = x\) is continuous.

  • Resolution

    It is sufficient to verify that any open set is an open set under id.

Difficulty level: Easy task (using definitions and simple reasoning)
Proving or derivation task
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