Given a pair of continuous functions from a topological space to an ordered set, how to prove that this set is closed?
10180
How to prove that this set is closed?
16735
If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed
27661
The closed graph theorem in topology
128482
The set of subsequential limits is closed
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
130299
Prove that if a function $f: X\to Y$ continuous then its graph is closed
127900
Interior of closure of open set in topological space
3649
Closed unit interval is connected proof
153495
Continuous function does not map closed set to closed set
127739
Is a continuous function on a bounded set bounded itself?
153256
Compact topological space with closed graph implies continuity
108734
$T$ is continuous if and only if $\ker T$ is closed
131992
A problem on continuous functions
14896
Prove: the set of zeros of a continuous function is closed.
146707
Formally show that the set of continuous functions is not measurable
143457
Is product of two closed sets closed?
136851
Proof that the set of subsequential limits is closed