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.

What is the importance of the stone Cech compactification?

The Stone-Čech compactification is considered to be one of the more important universal properties in topology due to its importance in applications that range from Ramsey Theory1 and Topological Dynamical Systems to computing the dual space of l∞(R), the space of bounded sequences of real numbers.

What does compactification mean?

1 : a compact topological space that contains a given topological space as a subset or that contains a subset homeomorphic to the given topological space.