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A function ''f'' from a [[topological space]] ''A'' to a topological space ''B'' is called '''locally constant''', iff for every ''a'' in ''A'' there exists
Every locally constant function from the [[real number]]s '''R''' to '''R''' is constant. But the function ''f'' from the rationals '''Q''' to '''R''', defined by ''f''(''x'') = 0 for ''x'' < π, and ''f''(''x'') = 1 for ''x'' > π, is locally constant.
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