limit point

Definitions

Given a subset S of a given topological space T, any point p whose every neighborhood contains some point, distinct from p, which belongs to S.

Equivalents

Examples

“is an example of a function having infinitely many essential singularities with a limit⟳ point⟳ at z=0. It is an easy matter⟳ to give⟳ examples of "elementary" functions whose singularities have⟳ a countable number⟳ of limit⟳ points.”

“If z_0 is a limit⟳ point⟳ of S, then every ϵ-neighborhood of z_0 must contain⟳ infinitely many points of S.”

“As the next example shows, the set⟳ of zeros may well have⟳ a limit⟳ point⟳ not belonging to the domain.”

CEFR level