Compactification (mathematics)

This is the compactification in the plane of the graph of sin(1/x) over the interval (0,2/π], with a judiciously chosen arc from (0,-1) to (2/π,1).
This is the compactification in the plane of the graph of sin(1/x) over the interval (0,2/π], with a judiciously chosen arc from (0,-1) to (2/π,1).

In mathematics, in general topology, compactification is the process or result of making a topological space into a compact space. A compact space is a space in which every open cover of the space contains a finite subcover. The methods of compactification are various, but each is a way of controlling points from "going off to infinity" by in some way adding "points at infinity" or preventing such an "escape".

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