 End (topology)

An end of a noncompact topological space describes a coherent way to escape every compact subset. For a cofinal compact exhaustion, when one exists, $K_1\subseteq K_2\subseteq \cdots$, it is represented by nested connected components of the complements. A connected noncompact manifold is disconnected at infinity when it has more than one end.

In topology, the concept of an "end" provides a way to classify the asymptotic behavior of a space at infinity. More formally, an end of a topological space can be understood as a way to describe how the space can be "accessed" from large distances.