Prove that $g$ is continuous.
87239
Prove functions defined by sup and inf are continuous
62887
Proof that a linear transformation is continuous
62455
Prove Equivalence Relation in G
143174
property of continuous function
132478
Prove that continuous functions mapping irrationals to rationals must be constant
42084
Set of points of continuity are $G_{\delta}$
12408
Prove that a function whose derivative is bounded is uniformly continuous.
43874
Differentiability implies continuity - A question about the proof
13257
How to prove this problem about uniform continuity
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
130299
Prove that if a function $f: X\to Y$ continuous then its graph is closed
58664
Proving a function is continuous for a fixed variable
55238
Show that if $f:X\to Y$ is a continuous function if and only if the graph of $f$ is a closed subset of $X\times Y$
34940
Continuity of $f(x) = x^n$
125682
Proof verification: the product of two continuous functions is continuous
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
23845
How to prove the continuity of the metric function?