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
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“Capital is a result of labor, and is used by labor to assist it in further production. Labor is the active and initial force, and labor is therefore the employer of capital.”
—Henry George (1839–1897)