The etale space of a sheaf 
on a topological space 
is the disjoint
union of its stalks 
over all 
. A sheaf section 
over an open
set 
determines the set of germs 
, and these sets
form a topological 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 also be T2-spaces.
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