Limit point

A limit point¹ generalises convergence to a limit. Given a topological space $𝑋$ , a point $𝑎 \in 𝑋$ is called a limit point of a sequence $(𝑥 𝑛) \infty 𝑛 = 1$ iff every (open) neighbourhood from $𝑎$ contains infinite $𝑎 𝑛$ . topology Note that this does not imply $𝑥 𝑛 \to 𝑎$ , for examples the sequence defined by $𝑎 𝑛 = (- 1) 𝑛$ is not convergent but has limit points ${- 1, 1}$