In topology an related branches of mathematics, a totally bounded space, or precompact space (note though that some sources such as PlanetMath take precompact to mean relatively compact), is a space that can be covered by finitely many subsets of any fixed "size" (where the meaning of "size" depends on the given context). The smaller the size fixed, the more subsets may be needed, but any specific size should require only finitely many subsets. A related notion is a totally bounded set, or precompact set, in which only a subset of the space needs to be covered. Every subset of a totally bounded space is a totally bounded set; but even if a space is not totally bounded, still some of its subsets will be.