Lebl-Basic-Analysis-I · Problem 6.2.6

Sequences of Functions

Mathematics · uniform-convergence-discontinuous-functions

Problem

True/False; prove or find a counterexample to the following statement: If {fn}n=1∞\{f_n\}_{n=1}^\infty is a sequence of everywhere discontinuous functions on [0,1][0,1] that converge uniformly to a function ff, then ff is everywhere discontinuous.

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