Exercise 2.1.7 (Interior of a set)

Question

Show that if $S$ is a subset of a topological space $X$, then $\operatorname{int}(S)$ is the union of all open sets contained in $S$.

Elu Thingol · Accepted Answer

We have to demonstrate that
$$\operatorname{int}(S) = \bigcup \left\{ U \in \mathcal{T} \mid U \subset S \right\}.$$
But the equivalence follows directly from the definition of interior, since it contains all points $x \in S$ for which there is an open neighbourhood $S$ such that $U \subset S$.

Exercise 2.1.7 (Interior of a set)

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Exercise 2.1.7 (Interior of a set)

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