Suppose that "X" is a space of some sort. It is often the case that, at each "x" ∈ "X", the ring of germs of functions at "x" is a local ring. This is the case, for example, for continuous functions on a topological space; for "k"-times differentiable, smooth, or analytic functions on a real manifold (when such functions are defined); for holomorphic functions on a complex manifold; and for regular functions on an algebraic variety. The property that rings of germs are local rings is axiomatized by the theory of locally ringed spaces.