New posts in Continuity

Let $f$ be integrable on $[a,b]$ and suppose for each integrable function $g$ defined on $[a,b]$, $\int^{b}_afg=0$, then $f(x)=0,\forall x\in[a,b]$

If a function is continuous everywhere, but undefined at one point, is it still continuous?

Having trouble showing a function is continuous: $x/(1+|x|)$

Construct a continuous real valued function which takes zero on integers and such that image of function is not closed.

Is the derivative of a continuously differentiable function always integrable?

How is the discrete metric continuous?

An example of a group with a topology

If $f : [a,b]\to\Bbb R$ is continuous, are there $x_1,x_2\in (a,b)$ such that $\tfrac{f(b)-f(a)}{b-a} = \tfrac{f(x_1)-f(x_2)}{x_1-x_2}$?

Show that there is a continuous real function $h$ on $[0,1]$ such that $\lim \sup |\frac{h(x+t)-h(x)}{t}| = \infty$ for all $x \in [0,1)$

Continuous bijection which is not a homeomorphism.