Quotient topology

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In general topology, the quotient topology, or identification topology is defined on the image of a topological space under a function.

Let be a topological space, and q a surjective function from X onto a set Y. The quotient topology on Y has as open sets those subsets of such that the pre-image .

The quotient topology has the universal property that it is the finest topology such that q is a continuous map.

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