Theorems · Theorem · category theory
Opens.pretopology_toGrothendieck
∀ (T : Type u) [inst : TopologicalSpace T], (Opens.pretopology T).toGrothendieck = Opens.grothendieckTopology T
The pretopology associated to a space induces the Grothendieck topology associated to the space.
- Defined in
- Mathlib.CategoryTheory.Sites.Spaces
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- CategoryTheory.GrothendieckTopologystatement · cited by 1,415
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- Opens.grothendieckTopologystatement and proof · cited by 206
- GaloisInsertion.l_u_eqproof · cited by 37
- CategoryTheory.Pretopologyproof · cited by 32
- CategoryTheory.Pretopology.toGrothendieckstatement and proof · cited by 18
- Opens.pretopologystatement · cited by 2
- CategoryTheory.Pretopology.giproof · cited by 2
- Opens.toPretopology_grothendieckTopologyproof · cited by 1
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