 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2012/e/e3/a/iv/solution

A

is a point

x \in X

such that every open neighbourhood of

x

contains a point of

A

different from

x

x \in A^{'} ⟺ (U ∖ {x}) \cap A \neq = \emptyset for every open U ∋ x .

The point itself need not belong to

A

. Requiring a different point distinguishes accumulation from mere membership in the closure.

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