New posts in Continuity

Bounded linear map which is not continuous

Given $f(x)$ is continuous on $[0,1]$ and $f(f(x))=1$ for $x\in[0,1]$. Prove that $\int_0^1 f(x)\,dx > \frac34$.

Can any continuous function be re-parameterized into a differentiable function?

Is $f(x)=\sum_{n=1}^{\infty}\frac{x}{1+n^2x^2}$, $x\in[0,1]$ continuous on $[0,1]$

A trivial question about continuity

Can this function be defined in a way to make it continuous at $x=0$?

Prove that a function between metric spaces $(X,d_{X})$ and $(Y,d_{Y})$ is continuous iff the pre-image of open sets is open

Prove that there are an infinite number of discontinuities on this function.

$h:[0,1] \to\mathbb{R}$ continuous, and ivt

Does continous and convex on a closed interval imply Lipschitz?