![real analysis - Converge pointwise but not uniformly a problem from Axler 2020 - Mathematics Stack Exchange real analysis - Converge pointwise but not uniformly a problem from Axler 2020 - Mathematics Stack Exchange](https://i.stack.imgur.com/fp2LK.png)
real analysis - Converge pointwise but not uniformly a problem from Axler 2020 - Mathematics Stack Exchange
![MathType on Twitter: "When studying function sequences, pointwise convergence is not enough to ensure that sequences of continuous functions have a continuous limit. Uniform convergence is necessary to maintain this basic property, MathType on Twitter: "When studying function sequences, pointwise convergence is not enough to ensure that sequences of continuous functions have a continuous limit. Uniform convergence is necessary to maintain this basic property,](https://pbs.twimg.com/media/D0QrGURWsAAsarV.jpg)
MathType on Twitter: "When studying function sequences, pointwise convergence is not enough to ensure that sequences of continuous functions have a continuous limit. Uniform convergence is necessary to maintain this basic property,
![real analysis - Graphical Interpretation of Pointwise and Uniform Convergence of Functional Sequence - Mathematics Stack Exchange real analysis - Graphical Interpretation of Pointwise and Uniform Convergence of Functional Sequence - Mathematics Stack Exchange](https://i.stack.imgur.com/Wl9lZ.jpg)