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Mathster of the Universe | by Paul Slevin

Mathster of the Universe by Paul Slevin Skip to content HomeAbout A Universal Property of the Quotient Topology Posted on August 8, 2011 by Paul Okay, here we will explain that quotient maps satisfy a universal property and discuss the consequences. THEOREM: Let be a quotient map. Let be a topological space, and let be constant on the fibres of (that is ). Then there exists a unique continuous map such that . Proof: Existence first. Define by . This is well defined since and because is