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In the passage below, in the last paragraph, what is the meaning for the parenthesized bit - "notice we do not say fiber!".

Is what they mean "notice we did not say that the total space $E$ is the union of the fibers" ?

Cause honestly, I have given it some thought and I don't see why they couldn't have said that.

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Prince M
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    A fiber bundle is a particular type of etale map, so fibers are particularly nice stalks but not conversely. This is more general. – Randall Oct 25 '18 at 02:42
  • Huh there must be multiple definitions of fibers over a point because I have seen fibers over a point to be defined as literal pre images, exactly as a stalk is being described as above – Prince M Oct 25 '18 at 03:20
  • There is, but I don't think the super-general definition of fiber is all that fashionable anymore. Maybe it depends on the field (alg. topology vs. geometry). Anyway, clearly in nLab's exposition they want there to be a difference. – Randall Oct 25 '18 at 03:26
  • Ok thanks that makes sense – Prince M Oct 25 '18 at 03:50
  • This question is related: https://math.stackexchange.com/questions/2248922/fibre-of-a-sheaf-of-mathcalo-x-modules – Viktor Vaughn Oct 25 '18 at 03:58

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