| 11. | The " fibers " are by definition the subspaces of that are the inverse images of points of.
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| 12. | The flatness of ? ensures that the inverse image of " Z " continues to have codimension one.
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| 13. | Then Zariski's connectedness theorem says that the inverse image of any normal point of " Y " is connected.
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| 14. | The easy way to remember the definitions above is to notice that finding an inverse image is used in both.
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| 15. | A cartesian section is thus a ( strictly ) compatible system of inverse images over objects of " E ".
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| 16. | For example, it can be shown that an inverse image f ^ {-1 } [ 0 ] is a non-Borel set.
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| 17. | There are also domain to sheaves and morphisms on the codomain, and an inverse image functor operating in the opposite direction.
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| 18. | However, it is a direct consequence of the definition that two such inverse images are isomorphic in " F T ".
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| 19. | The twisted inverse image functor f ^ ! is, in general, only defined as a functor between Grothendieck duality and Verdier duality.
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| 20. | To do this requires two steps : First compute an inverse image of each point to be visited; then sort the values.
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