Basic Analysis I — Real Analysis · Problem 6.2.5

Sequences of Functions — Jiri Lebl

Mathematics — Real Analysis · pointwise-not-uniform-convergence

Problem

Find an example of a sequence of continuous functions on (0,1)(0, 1) that converges pointwise to a continuous function on (0,1)(0, 1), but the convergence is not uniform. Note: In the previous exercise, (0,1)(0, 1) was picked for simplicity. For a more challenging exercise, replace (0,1)(0, 1) with [0,1][0, 1].

Related theory

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