Let $A$ be a set of all continuous functions $f:[0,1] \to \mathbb R^+ \cup \{0\}$ that satisfies the following condition.
47211
Does $\varphi(x)\le\int_0^x\varphi(t)dt$ for all $x\in[0,\infty)$ imply $\varphi\equiv0$.
104044
Prove continuous functions $f$ and $g$ are equal
126821
Let $f:[0,1]\to \mathbb{R}$. Show that $\{a \in [0,1]: f(a)\neq 0\} = \bigcup_{n=1}^{\infty} \{a \in [0,1]: |f(a)|\geq 1/n\}$
13765
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
65946
A function $f: \mathbb R \to \mathbb R$ satisfies equation $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb R $
92089
If $f:[a,b]\to \mathbb{R}$ is continuous and nonnegative and $\int_a^b{f}=0$, then $f(x)=0$ for all $x\in [a,b]$
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
43189
Examples of continuous functions $f : \mathbb{R} \to \mathbb{R}$
38584
$T\colon L^2[0,1] \to L^2[0,1]$ be a bounded linear map of Hilbert spaces such that if $f\in L^2[0,1]$ is continuous then so is $Tf$.
90619
For closed subsets $A,B \subseteq X$ with $X = A \cup B$ show that $f \colon X \to Y$ is continuous iff $f|_A$ and $f|_B$ are continuous.
136583
Infimum is a continuous function, compact set
100839
If two continuous functions are equal almost everywhere on $[a,b]$, then they are equal everywhere on $[a,b]$
44144
If $f:[a,b]\to \mathbb R$ is continuous then so is $\max_{t\in [a,x]}f(t)$?
14896
Prove: the set of zeros of a continuous function is closed.
27800
For continuous function $ f:\mathbb S^1 \to \mathbb R$ there exists uncountably many distinct points $x,y$ such that $f(x)=f(y)$
39321
If $f:\mathbb R \to \mathbb R$ satisfies $f'(x) <L$ for some $L<1$, then $f$ has a unique fixed point
151573
Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.