category of open subsets
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Category of open subsets
Given a topological space , the category of open subsets of is the category whose
objects are the open subsets of ;
morphisms are the inclusions of open subsets into each other.
The category is a poset, in fact a frame (dually a locale): it is the frame of opens of .
The category is naturally equipped with the structure of a site, where a collection of morphisms is a cover precisely if their union in equals :
The category of sheaves on equipped with this site structure is usually written
Revised on August 31, 2012 14:27:37
by Urs Schreiber