Can the graph of a continuous real function be a totally disconnected subset of $\mathbb{R}^2$?
135863
Is the graph of a continuous function homeomorphic to its domain?
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
118048
Can a function with just one point in its domain be continuous?
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 ?
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
120947
continuous real-valued function
83204
Is every $G_\delta$ set the set of continuity points of some function $f$?
155794
Are the complements of two homeomorphic compact, connected subsets of $\mathbb{R}^2$ homeomorphic?
109374
Is the Discrete Topology on $X$ the Only One Containing All Infinite Subsets of $X$?
19754
$\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
151358
Continuous image of a locally connected space which is not locally connected
5295
Can the graph of a bounded function ever have an unbounded derivative?
73594
Existence of continuous function $f$ on $\Bbb R$ which vanishes exactly on $A\subset \Bbb R$
95321
Subspaces of all real-valued continuous functions on $\mathbb{R}^1$
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
149095
$f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
16735
If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed