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Quotient space

Definition

Given a topological space (X,T) and an equivalence relation ~, the quotient space (X/~,T') is given by:

• X/~ is the set of equivalence classes.
• T', the quotient topology, is the set of subsets U of X/~ where $\bigcup_{[x] \in U} [x] \in T$.

Properties

all these pages adapted with probably insufficient credit from my university's lecture notes