In general topology and related areas of mathematics, the initial topology (or weak topology or limit topology or projective topology) on a set, with respect to a family of functions on, is the coarsest topology on X which 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.
The dual construction is called the final topology.
Read more about Initial Topology: Definition, Examples, Categorical Description
Famous quotes containing the word initial:
“For those parents from lower-class and minority communities ... [who] have had minimal experience in negotiating dominant, external institutions or have had negative and hostile contact with social service agencies, their initial approaches to the school are often overwhelming and difficult. Not only does the school feel like an alien environment with incomprehensible norms and structures, but the families often do not feel entitled to make demands or force disagreements.”
—Sara Lawrence Lightfoot (20th century)