Showing that $\{x\mid f(x)\leq g(x)\}$ is closed.
46287
Let $Y$ be an ordered set in the order topology with $f,g:X\rightarrow Y$ continuous, show that $\{x:f(x)\leq g(x)\}$ is closed in $X$
43431
Show that $F+G$ is closed when $G$ a closed subspace of normed space $E$ and $F$ a finite dimensional subspace of $E$.
144589
Proving that if $f(x) \le g(x)$ then $f(x_0) \le g(x_0)$
130975
Given a pair of continuous functions from a topological space to an ordered set, how to prove that this set is closed?
82371
$f$ is an entire function with Im $f\geq 0$
43956
Differentiating $f(x)^{g(x)}$
91682
Graph of a continuous function is closed
66531
$\|h(x)-h(y)\|\geq 3\|x-y\|$ prove that image of open is open
86105
Can $\{(f(t),g(t)) \mid t\in [a,b]\}$ cover the entire square $[0,1] \times [0,1]$ ?
102170
Showing a Sequence and its Limit are Closed
144353
A closed ball in a metric space is closed
47680
Prove that the union of the interior of a set and the boundary of the set is the closure of the set
119105
If $(X,d)$ is a complete metric space and $A$ is closed then show that for $x \in X$ there exists an element $a_0 \in A$ such that $d(x,A)=d(x,a_0)$
158569
Proving a particular subset of $R^n$ is closed
35573
A closed ball in a metric space is a closed set
84512
The preimage of continuous function on a closed set is closed.
10236
Show that $a^n \mid b^n$ implies $a \mid b$