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Line 22: In general, if ''E'' is any subset of a [[topological space]] ''X'' such that both ''E'' and the complement of ''E'' are dense in ''X'', then the real-valued function which takes the value 1 on ''E'' and 0 on the complement of ''E'' will be nowhere continuous. Functions of this type were originally investigated by [[Johann Peter Gustav Lejeune Dirichlet\|Dirichlet]]. ==See also== *[[popcorn function]] ==References==

Nowhere continuous function: Difference between revisions