Why is the graph of a continuous function to a Hausdorff space closed?
113022
Is the graph $G_f=\{(x,f(x)) \in X \times Y\ : x \in X \}$ a closed subset of $X \times Y$?
81488
If a continuous function$f: (X, \mathscr T_X) \to (Y, \mathscr T_Y)$ is injective (Given $Y$ is Hausdorff), show that X is hausdorff
154682
G/H is Hausdorff implies H is closed (General topology, Volume 1 by N. Bourbaki)
65180
A compact Hausdorff space that is not metrizable
49099
Constructing a continuous function whose graph seems 'special'
142459
Continuity of a Function in Terms of Closure and Interior
97761
Show that a proper continuous map from $X$ to locally compact $Y$ is closed
105333
Generated $\sigma$-algebras with cylinder set doesn't contain the space of continuous functions
144353
A closed ball in a metric space is closed
33114
Uniqueness of a continuous extension of a function into a Hausdorff space
16743
Graph of real continuous function has measure zero
157603
Continuity $\iff$ Preimage is closed whenever set is closed
35573
A closed ball in a metric space is a closed set
10747
Given function $g$ continuous in line $[0,\infty)$...
121135
Why don't we use closed covers to define compactness of metric space?
134575
Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
31266
Proof of "the continuous image of a connected set is connected"