natural topology

In any domain of mathematics, a space has a natural topology if there is a topology on the space which is "best adapted" to its study within the domain in question. In many cases this imprecise definition means little more than the assertion that the topology in question arises naturally or canonically (see mathematical jargon) in the given context. Note that in some cases multiple topologies seem "natural". For example, if Y is a subset of a totally ordered set X, then the induced order topology, i.e. the order topology of the totally ordered Y, where this order is inherited from X, is coarser than the subspace topology of the order topology of X.