How do you prove the set $G = \{(x, f(x)) \mid x \in \mathbb R\}$ is closed?
91682
Graph of a continuous function is closed
84512
The preimage of continuous function on a closed set is closed.
108740
$C^1[a,b]$ is closed in $C[a,b]$
152976
Real Analysis: open and closed sets
97316
Let $F : X → X$ be continuous. Prove that the set $\{x ∈ X : F(x) = x\}$ of fixed points of F is closed in X
158155
Is set of isolated points of S closed?
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
126897
Showing the set $A+B$ is closed.
40162
Prove that the set $\mathbb{Q}[\alpha] = \{a+b\alpha+c\alpha^2 \mid a, b, c \in\mathbb{Q}\}$ is closed under addition and multiplication.
16735
If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed
140103
If product of two sets $A\times B$ is closed, are $A$ and $B$ closed?
104016
Limit point of the set $G= \{1/n: n \in \mathbb N\}$?
106957
Compact sets are closed?
125962
The set $A'$ is closed in a $T_1$ space
21820
How to prove that a set is invariant?
158569
Proving a particular subset of $R^n$ is closed
128482
The set of subsequential limits is closed