Theorems · Theorem · general topology
SeparationQuotient.preimage_image_mk_open
∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X},
IsOpen s → SeparationQuotient.mk ⁻¹' SeparationQuotient.mk '' s = s- Defined in
- Mathlib.Topology.Inseparable
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.imagestatement and proof · cited by 5,609
- Set.preimagestatement and proof · cited by 4,946
- IsOpenstatement and proof · cited by 2,400
- Set.Subset.antisymmproof · cited by 213
- SeparationQuotientstatement · cited by 128
- SeparationQuotient.mkstatement and proof · cited by 94
- Set.subset_preimage_imageproof · cited by 44
- Inseparable.mem_open_iffproof · cited by 11
- SeparationQuotient.mk_eq_mkproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- SeparationQuotient.isInducing_mkproof · cited by 7
- SeparationQuotient.isOpenMap_mkproof · cited by 5