9 results about "Initial topology" patented technology

In general topology and related areas of mathematics, the initial topology (or weak topology or limit topology or projective topology) on a set X, with respect to a family of functions on X, is the coarsest topology on X that makes those functions continuous. The subspace topology and product topology constructions are both special cases of initial topologies. Indeed, the initial topology construction can be viewed as a generalization of these.