In this chapter we introduce some topologies on the category of algebraic spaces. Compare with the material in [SGA1], [Ner], [LM-B] and [Kn]. Before doing so we would like to point out that there are many different choices of sites (as defined in Sites, Definition 7.6.2) which give rise to the same notion of sheaf on the underlying category. Hence our choices may be slightly different from those in the references but ultimately lead to the same cohomology groups, etc.
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