Sequence

Limit point

A limit point¹ generalises convergence to a limit. Given a topological space , a point is called a limit point of a sequence iff every (open) neighbourhood from contains infinite . #m/def/topology Note that this does not imply , for examples the sequence defined by is not convergent but has limit points

Properties

• Limit points are points contained in the closure of every end piece
• Limit points are limits of convergent subsequences in a first-countable space

#state/tidy | #lang/en | #SemBr