continuity of $f ' $
16291
Discontinuous derivative.
71487
Real Analysis: Continuity of a Composition Function
29154
$f$ is continuous and open implies $f$ injective
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
125745
continuity of power series
98772
Continuity of a function in $\mathbb{R}$
129073
If $f'$ is bounded, then $f$ is uniformly continuous
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
93021
$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$
145368
How to show $f:Y\to X^{+}$ is continuous?
112409
If $f$ is continuous and $f'(x)\ge 0$, outside of a countable set, then $f$ is increasing
53738
Monotone functions and continuity
104263
How to show that $f'(x)<2f(x)$
95429
If $f$ is continuous with $ \int_0^{\infty}f(t)\,dt<\infty$ then which are correct?
136011
Must $f$ be continuous?
121957
Is $p\mapsto \|f\|_p$ continuous?
151573
Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.