New posts in Continuity

Weak lower semicontinuity of functional with two arguments

A challenging problem on continuity-MADHAVA-2020.

Are "locally continuous" functions continuous?

How to prove that if $f:\mathbb{R} \rightarrow \mathbb{R}$ is continuous and $|f(x) - f(y)| > |x-y|$ for all $x,y$,then range of $f$ is $\mathbb{R}$

Do the closed unit disk $D$ and $f(D)$ intersect, if $||f(x)-x||\le2$ for all $x\in D$?

recursive sequence with continuous function

Function defined everywhere but continuous nowhere

Let $f:[0,n]\to \Bbb R$ be continuous with $f(0)=f(n)$. Then there are $n$ pairs of numbers $x,y$ such that $f(x)=f(y)$ and $y-x\in\Bbb N$.

Uniformly Continuous on $C^1[a,b]$

$X \subset \mathbb{R}^n$ bounded $\implies f(X)$ is Bounded