Interior And Closure

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Definition (Interior And Closure)

Let $A$ be a subset of the real numbers.

• We use the notation $A'$ to denote the set of limit points of $A$.
• The closure of $A$, written $\text{cl}(A)$, is the union of $A$ and its limit points, so $\text{cl}(A) = A\cup A'$.
• The interior of $A$, written $\text{int}(A)$, is the collection of interior points of $A$.