What is "compactification"

n. 1 (context topology English) Any of various procedures of enlarging a topological space to make it compact. 2 (context topology English) The space resulting from any such procedure. 3 (context physics English) Any modification of a theory such that an infinite parameter becomes finite

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".

In physics, compactification means changing a theory with respect to one of its space-time dimensions. Instead of having a theory with this dimension being infinite, one changes the theory so that this dimension has a finite length, and may also be periodic.

Compactification plays an important part in thermal field theory where one compactifies time, in string theory where one compactifies the extra dimensions of the theory, and in two- or one-dimensional solid state physics, where one considers a system which is limited in one of the three usual spatial dimensions.

At the limit where the size of the compact dimension goes to zero, no fields depend on this extra dimension, and the theory is dimensionally reduced.

Compactification may refer to:

• Compactification (mathematics), making a topological space compact
• Compactification (physics), the "curling up" of extra dimensions in string theory
• Compaction (disambiguation)