If $x$ is an isolated point of $S \subseteq \mathbb{R}$, then $x$ is a boundary point of $S$.
35751
Is There a Problem with This Professor's Proof Concerning Interior and Boundary Points?
33734
Every closed subset $E\subseteq \mathbb{R}^n$ is the zero point set of a smooth function
59275
If $X$ is an infinite set, then $X$ with the discrete topology is not compact
40232
What do we mean when we say "Let $x$ be an element of the set $\mathbb{R}$"?
65358
Prove $X$ is compact iff for each family $\{ F_\alpha\}_{\alpha\in I}$ of closed subsets of $X$ with the FIP, we have $\cap F_\alpha\neq\varnothing$.
61375
Meaning of $\mathbb{R}[x]$
152784
$f \in {\mathscr R[a,b]} \implies f $ has infinitely many points of continuity.
47810
$C(X)$ is separable when $X$ is compact?
144246
Subset of $\mathbb{R}^n$ homeomorphic to $\mathbb{R}^n$
136158
$X$ has Indiscrete topology $\implies$ any subset of $X$ is connected
2575
Showing that $\mathbb{R}$ is connected
32534
Prove that a set $S \subseteq \mathbb{R}$ is closed and bounded if and only if every sequence in $S$ has a sub sequence converging to a point of $S$.
83009
Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
105445
Are the rationals a closed or open set in $\mathbb{R}$?
41997
Can the boundary of a set be ignored, when integrating over it.
56728
Question about limit points of a Subset of $\mathbb{R}$
69650
In $\mathbb{R}^n$, locally lipschitz on compact set implies lipschitz