A map can be open, closed and continuous indepently.
2198
Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
128482
The set of subsequential limits is closed
116009
Proving that if a set is both open and closed then it is equal to the real numbers
54222
Prove the map has a fixed point
147247
Continuous function on closed unit ball
104769
Any two points in a Stone space can be disconnected by clopen sets
128069
Continuity in Slices + Mapping Compact Sets to Compact Sets = Continuous
52388
The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition
137460
How should I think of an open vs. closed set?
90619
For closed subsets $A,B \subseteq X$ with $X = A \cup B$ show that $f \colon X \to Y$ is continuous iff $f|_A$ and $f|_B$ are continuous.
24050
Characterization of the Closure of a Set
47
Let $f$ be a continuous and open map from $\mathbb R $ to $\mathbb R$.Prove that $f$ is monotonic.
29154
$f$ is continuous and open implies $f$ injective
86782
A $T_4$ space satisfying that 'every continuous map from it to a Hausdorff space is a closed map' is compact.
91682
Graph of a continuous function is closed
157578
perfect map in topology
108734
$T$ is continuous if and only if $\ker T$ is closed