No. of $t,s \in [0,1]$ such that $f(t)=f(s)$ for a continuous function $f:[0,1]\rightarrow [0,1]$
131992
A problem on continuous functions
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
129551
Does $\lim_{h\rightarrow 0}\ [f(x+h)-f(x-h)]=0$ imply that $f$ is continuous?
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
44144
If $f:[a,b]\to \mathbb R$ is continuous then so is $\max_{t\in [a,x]}f(t)$?
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
50649
On the existence of a continuous bijection $f\colon [0,1]\to [0,1]\times [0,1]$
16338
3rd iterate of a continuous function equals identity function
95469
Suppose $f:[0,1] \Rightarrow \mathbb{R}$ is continuous and $\int_0^x f(x)dx = \int_x^1 f(x)dx$. Prove that $f(x) = 0$ for all $x$
10747
Given function $g$ continuous in line $[0,\infty)$...
104510
For continuous $f$, $\int_0^x f(t)dt = ∫_x^1f(t)dt$ implies $f=0$.
29582
Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$
151573
Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.
44057
Pointwise but not uniform convergence of continuous functions on $[0,1]$
149907
$T\circ T=0:V\rightarrow V \implies R(T) \subset N(T)$
14516
The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
84510
If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant