does $f(x,y)$ continuous imply $\int_{a}^{b} f(x,y) \,dx $ is continuous with respect to y?
39235
Argue that the iterated integral of a continuous function is continuous
37966
If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$
150770
Why is $f^n(\xi(x))$ continuous over $x$?
130299
Prove that if a function $f: X\to Y$ continuous then its graph is closed
22061
$|f(x)-f(y)|\geq k|x-y|$.Then $f$ is bijective and its inverse is continuous.
44144
If $f:[a,b]\to \mathbb R$ is continuous then so is $\max_{t\in [a,x]}f(t)$?
52922
let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
37850
Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval?
149399
Given continuous $f$ and $g$, there exists $c \in (a,b)$ such that $\int_{a}^{c} f(x) \ \mathrm dx = \int_{c}^{b} g(x) \ \mathrm dx$
141945
Why is $f(x) = \sqrt{x}$ is continuous at $x=0$? Does $\lim_{x \to 0^{-}} \sqrt{x}$ exist?
32571
Is the maximum function of a continuous function continuous?
19072
$\int_{\mathbb R} |f(x)| dx < \infty \implies \int^{\infty}_{n} |f(x)| dx \to 0$ as $n \to \infty$?
143174
property of continuous function
141842
Is the convolution of two continuous functions continuous?
153957
Bounded variation and $\int_a^b |F'(x)|dx=T_F([a,b])$ implies absolutely continuous
50725
Inverse of function is continuous or not?
12523
Supremum of a Continuous Function is Continuous