If $f$ is continuous, then $X$ and $\{(x,f(x)); x\in X\}$ (the domain and the graph of $f$) are homeomorphic
2093
If $f$ is continuous then $G$ is homeomorphic to $X$.
150554
proof that $f'$ is continuous at $a$
121708
$S := \{x \in \Bbb R^3: ||x||_2 = 1 \}$ and $T: S^2 \to \Bbb R$ is a continuous function. Is $T$ injective?
93021
$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
155923
continuity of $f(x,y)$ in $\mathbb R^2$.
128911
Continuous extension of a real function
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
126461
Show that $g:I\to\mathbb{R}$ is continuous and $f:(x-x_0)g(x)$ is differentiable
77621
Continuity of function mapping connected set to connected set
16735
If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed
142459
Continuity of a Function in Terms of Closure and Interior
122086
continuous function: preimage of closure of a set is closure of preimage
126463
Can open sets and closed sets of $\mathbb{R}^n$ be homeomorphic?
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 ?
124444
If $f$ s discontinuous at $x_0$ but $g$ is continuous there, then $f+g$?
37966
If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$