Answer to Question #282265 in Differential Geometry | Topology for Satya

Question

$\text { Find the interior Int }\left\{\frac{1}{n} \mid n \in \mathbb{N}\right\} \text { of a subset of } \mathbb{R} \text {. }$ (DG)

Answer 1

interior of a subset S of a topological space X is the union of all subsets of S that are open in X.

let $S=\{\frac{1}{n}|n\isin N\}$

for every $x=1/n\isin S$ , every neighborhood $N(1/n,\varepsilon)$ contains irrational numbers (i.e. numbers not in S) so x is not an interior point. Thus, $Int\ S=\empty$