query: Does pointwise convergence to a continuous function on a closed interval imply uniform convergence?
positive_passages.docid: 151832
positive_passages.text: uniformly convergence on compact metric space
negative_passages.docid: 140445
negative_passages.text: Sequence of continuous functions whose pointwise limit is discontinuous
negative_passages.docid: 95869
negative_passages.text: If continuity preserves convergence, and Cauchy sequences are convergent sequences, why do we need uniform continuity to preserve Cauchy sequences?
negative_passages.docid: 151936
negative_passages.text: Pointwise Convergence and Convergence in the mean of Riemann-integrable functions
negative_passages.docid: 158344
negative_passages.text: Uniform continuous maps that converge uniformly to a function f. What can we say about f?
negative_passages.docid: 40297
negative_passages.text: Proof of uniform limit of Continuous Functions
negative_passages.docid: 44057
negative_passages.text: Pointwise but not uniform convergence of continuous functions on $[0,1]$
negative_passages.docid: 140972
negative_passages.text: Uniform convergence of harmonic functions to $0$ on compact subsets
negative_passages.docid: 142645
negative_passages.text: $f_n$ converges uniformly on $[a,b]$ to some function $f$
negative_passages.docid: 55749
negative_passages.text: Compactly supported continuous function is uniformly continuous
negative_passages.docid: 4157
negative_passages.text: Function Sequence Uniform Convergence
negative_passages.docid: 129757
negative_passages.text: Uniformly convergent implies equicontinuous
negative_passages.docid: 110415
negative_passages.text: Proving a sequence of step functions converges pointwise to a function $f$.
negative_passages.docid: 119348
negative_passages.text: Find sequence of differentiable functions $f_n$ on $\mathbb{R}$ that converge uniformly, but $f'_n$ converges only pointwise
negative_passages.docid: 77239
negative_passages.text: Limit point versus limit and implications for convergence
negative_passages.docid: 126212
negative_passages.text: Proving uniform continuity on an interval
negative_passages.docid: 54600
negative_passages.text: Is a convex and lower semicontinuous function defined on a closed and convex subset of $\mathbb{R}^n$ continuous?