End (topology)

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.

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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 \dots

, 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.