Sheaf definition(s)??

2 Mar 2002

      Hello Cat community,

   I have been reading beginning Sheaf theory. The
definition of a sheaf varies somewhat from Goldblatt
to others.

             h
      A----------->B
       \          /
        \        /
         \      /
       f  \    / g
           \  /
            \/
             v
             X

    where A, B, and X are topological spaces and X is
    fixed

Goldblatt: An object is an ordered pair (A, f) where
             A is a topological space and f is
             continuous and an etale/local 
             homeomorphism

Other books: The continuity requirement for "f" is 
                dropped. 

Why the difference? I don't see that "etaleness" =>
   continuity.

Regards, Bill Halchin

Sheaf definition(s)??

Galchin Vasili