 Whether a set is closed depends on the space in which it is embedded.However, the compact Hausdorff spaces are "absolutely closed", in the sense that, if you embed a compact Hausdorff space "K" in an arbitrary Hausdorff space "X", then "K" will always be a closed subset of "X"; the "surrounding space" does not matter here.Stone-Čech compactification, a process that turns a completely regular Hausdorff space into a compact Hausdorff space, may be described as adjoining limits of certain nonconvergent nets to the space.