Concept

Adherent point

Summary
In mathematics, an adherent point (also closure point or point of closure or contact point) of a subset A of a topological space X, is a point x in X such that every neighbourhood of x (or equivalently, every open neighborhood of x) contains at least one point of A. A point x \in X is an adherent point for A if and only if x is in the closure of A, thus :x \in \operatorname{Cl}_X A if and only if for all open subsets U \subseteq X, if x \in U \text{ then } U \cap A \neq \varnothing. This definition differs from that of a limit point of a set, in that for a limit point it is required that every neighborhood of x contains at least one point of A x. Thus every limit point is an adherent point, but the converse is not true. An adherent point of A is either
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading