# real analysis – Convergent function sequence by point with a uniformly convergent subsequence.

Let $$f_n colon [0,1] to mathbb {R}$$ be a sequence of continuous functions that converge point to a continuous function $$f$$. Yes $${f_n }$$ has a uniformly convergent subsequence $${f_ {n_k} }$$, does that imply that $$f_n$$ converges uniformly towards $$f$$. If the answer is "no", please give me an example. Thanking you in advance.