How to prove a set of solution of a continuous function is closed?
14896
Prove: the set of zeros of a continuous function is closed.
104044
Prove continuous functions $f$ and $g$ are equal
35855
Closed form for an infinite product
55614
Prove that a set consisting of a sequence and its limit point is closed
87239
Prove functions defined by sup and inf are continuous
122190
Kernel of $T$ is closed iff $T$ is continuous
47680
Prove that the union of the interior of a set and the boundary of the set is the closure of the set
2142
Finding a set of continuous functions with a certain property 2
97761
Show that a proper continuous map from $X$ to locally compact $Y$ is closed
130916
Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$
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 $X$
110744
How to prove that a compact set in a Hausdorff topological space is closed?
64260
Prove that a function between metric spaces is continuous iff the inverse image of a closed set is closed
70959
Prove that a set $E$ is closed iff it's complement $E^{c}$ is open
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 $X\times Y$
131992
A problem on continuous functions
78300
Showing a set is closed other than giving a counterexample?