Is $\mathbb{R}\setminus\{0\}$ endowed with $d(x,y)=|\frac{1}{x}-\frac{1}{y}|$ complete?
16060
Showing this metric space is complete
1591
What does $\mathbb{R} \setminus S$ mean?
155066
Dimension of the quotient space $\frac{C_{0}}{M}.$
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
94218
Showing $d(x,y) = \frac{|x-y|}{1+|x-y|}$ is a distance.
54791
Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
23837
Why is $\mathbb{R}/{\sim}$ not first countable at $[0]$, where $x \sim y \Leftrightarrow x = y\text{ or }x,y \in \mathbb{Z}$?
85076
Is it true that $d(x,Y)=d(x,y_0)$ for some $y_0 \in Y$ when $Y$ is closed?
14345
If $A\subset\mathbb{R^2}$ is countable, is $\mathbb{R^2}\setminus A$ path connected?
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
51227
Proving that given metric space is complete: $X := (0,\infty)$ and $d:=|\ln(x)-\ln(y)|$
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
19754
$\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
1117
Is there a bijection between $(0,1)$ and $\mathbb{R}$ that preserves rationality?
34177
Prove that $\mathbb{R}^2\setminus\mathbb{Q}^2$ is connected without path connectedness
5625
Entire function with vanishing derivatives?