Limit Points & Boundaries – Lecture 11 (Topology)

A point x in a topological space X is a limit point of A ⊆ X exactly when:

1. A.x lies in A and every neighborhood of x is a subset of A
2. B.Every neighborhood of x intersects A at some point other than x
3. C.Some neighborhood of x is entirely contained in A
4. D.x is the limit of every sequence whose terms lie in A