Quotient space of an algebraic stack

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 formula_1 for some open substack "U" of "F".
The construction formula_2 is functorial; i.e., each morphism formula_3 of algebraic stacks determines a continuous map formula_4.
An algebraic stack "X" is punctual if formula_5 is a point.
When "X" is a moduli stack, the quotient space formula_5 is called the moduli space of "X". If formula_3 is a morphism of algebraic stacks that induces a homeomorphism formula_8, then "Y" is called "a" coarse moduli stack of "X". ("The" coarse moduli requires a universality.)