Locally constant function: Difference between revisions

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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 an environmentneighborhood ''U'' of ''a'', such that ''f'' is constant in ''U''.

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''<Pi, and ''f''(''x'')=1 for x>Pi, is locally constant.