Is $\text{Sup}f(x)$ continuous?
94781
Prove that $M(t)=\sup_ {a \leq x \leq t} f(x)$ given $f(x)$ is continuous on $[a,b]$
79307
How to analyze $\sup_{x>0}|e^xf(x)| < \infty$ and $\sup_{n\in\mathbb{N}} |f^{(n)}(0)|< \infty$?
130916
Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$
127739
Is a continuous function on a bounded set bounded itself?
115417
Continuity of $L^1$ functions with respect to translation
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
23436
$f$ Holder continuous with Holder exponent $p>1\implies f \text{ is constant}$
59519
What about the continuity of these functions in the uniform topology?
44144
If $f:[a,b]\to \mathbb R$ is continuous then so is $\max_{t\in [a,x]}f(t)$?
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
124444
If $f$ s discontinuous at $x_0$ but $g$ is continuous there, then $f+g$?
37850
Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval?
154881
Question on differentiability of a continuous function
97772
An example of a function which satisfies $\sup_{y}\inf_{x}f(x,y)<\inf_{x}\sup_{y}f(x,y)$
143618
If a function $f$ is continuous $\implies$ $|f|$ is continuous.(Answered by Myself)
100740
proof of that a continuous function has a fixed point
44574
Continuity of absolute value of a function