The etale space of a sheaf 
on a topological space 
is the disjoint union of its stalks 
over all 
. A section 
over an open set 
determines the set of germs 
, and these sets form a basis for the topology on
the etale space. The projection that sends each germ in 
to 
is a local homeomorphism. An etale space need not be a T2-space,
but etale spaces can be Hausdorff.
Etale Space
See also
Sheaf, Stalk, T2-SpacePortions of this entry contributed by Todd Rowland
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Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Etale Space." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EtaleSpace.html