In algebraic geometry, the quotient space of an algebraic stack F, denoted by |F|, is a topological space which as a set is the set of all integral substacks of F and which then is given a "Zariski topology": an open subset has a form for some open substack U of F.[1]
The construction is functorial; i.e., each morphism of algebraic stacks determines a continuous map .
An algebraic stack X is punctual if is a point.
When X is a moduli stack, the quotient space is called the moduli space of X. If is a morphism of algebraic stacks that induces a homeomorphism , then Y is called a coarse moduli stack of X. ("The" coarse moduli requires a universality.)
^In other words, there is a natural bijection between the set of all open immersions to F and the set of all open subsets of .
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