Prove that $f: \mathbb{R} \ni x \mapsto \left(x-x_{0}\right) \cdot g(x) \in \mathbb{R}$ is continuous
53497
Prove that the function is continuous and differentiable (not as easy as it sounds imo)
150554
proof that $f'$ is continuous at $a$
37966
If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$
53349
Prove that $\sqrt{x}$ is continuous on its domain $[0, \infty).$
154559
For each $x\in X$ there exists a neighborhood of x s.t $A\cap U\neq \emptyset$ for only finitely many $A\in\mathcal{A}$. Show that f is continuous.
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
64260
Prove that a function between metric spaces is continuous iff the inverse image of a closed set is closed
75479
Proving that this function is continuous on $G\times G$
149354
Proof of continuity $f(x+y) = f(x) + f(y)$
121957
Is $p\mapsto \|f\|_p$ continuous?
2093
If $f$ is continuous then $G$ is homeomorphic to $X$.
58664
Proving a function is continuous for a fixed variable
147299
Prove that $g(x,y) = \frac{x^3y}{x^2+y^2}$ with $g(0,0)=0$ is continuous
34940
Continuity of $f(x) = x^n$
104044
Prove continuous functions $f$ and $g$ are equal
140052
Show that $f(X - D) \cap f(D) = \varnothing$ with $f$ continuous in $X$, $D$ dense in $X$ and $f|_{D}$ homeomorphism
130023
Prove that the sum of two continuous functions is continuous