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".This is still imprecise, even once one has specified what the natural maps are, because there may be many topologies with the required property.Two of the simplest examples are the natural topologies of subspaces and quotient spaces.