Closed and connected graph of a function implies continuous function
86472
$f:\mathbb R \to \mathbb R^n$ be such that $G(f):=\{(x,f(x)):x \in \mathbb R\}$ is closed and connected in $\mathbb R^{n+1}$ , is $f$ continuous ?
153256
Compact topological space with closed graph implies continuity
140929
Increasing, continuous function implies connectivity and viceversa.
51156
Function is Continuous When Restricted to Closed Sets Which Cover the Space
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
64619
Continuity of a function of product spaces
12523
Supremum of a Continuous Function is Continuous
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
64487
Continuous function and dense set
155923
continuity of $f(x,y)$ in $\mathbb R^2$.
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
122086
continuous function: preimage of closure of a set is closure of preimage
12349
a construction of a continuous function from a normal space to [0,1]
40208
Locally Constant Functions on Connected Spaces are Constant
108734
$T$ is continuous if and only if $\ker T$ is closed
20688
Discontinuous functions with closed graphs
16743
Graph of real continuous function has measure zero