\[ x \in \operatorname{int}(A) \iff \exists \varepsilon > 0 : B_\varepsilon(x) \subset A \]

\[ x \in \partial A \iff \forall \varepsilon > 0 : B_\varepsilon(x) \cap A \neq \varnothing \land B_\varepsilon(x) \cap A^c \neq \varnothing \]

\[ x \in \operatorname{ext}(A) \iff \exists \varepsilon > 0 : B_\varepsilon(x) \subset A^c \]