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A set of equivalence classes supplied with the quotient topology, in which a subset is open exactly when its inverse image under the quotient map is open.
topology-without-tearshatcher-algebraic-topologyEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The equivalence relation determines the quotient-set representatives; the topology is then the finest topology making the quotient map continuous.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
topology-without-tearsThis is an authored directed relation from the source endpoint to the target endpoint.
Given a topological space and an equivalence relation, replace points by their equivalence classes and declare open in exactly when its quotient-map preimage is open in .
Identify elements by a stated equivalence relation and equip the quotient with the induced structure. The edge detail must state the representatives and equivalence relation.
topology-without-tearshatcher-algebraic-topologyEach relation below starts at this concept.
No direct relations are authored in this direction.