Page "Compactification (mathematics)" Paragraph 1

Consider the real line with its ordinary topology.

This space is not compact ; in a sense, points can go off to infinity to the left or to the right.

It is possible to turn the real line into a compact space by adding a single " point at infinity " which we will denote by ∞.

The resulting compactification can be thought of as a circle ( which is compact as a closed and bounded subset of the Euclidean plane ).

Every sequence that ran off to infinity in the real line will then converge to ∞ in this compactification.