Theorems · Theorem · general topology
SeparationQuotient.isInducing_mk
∀ {X : Type u_1} [inst : TopologicalSpace X], Topology.IsInducing SeparationQuotient.mk- Defined in
- Mathlib.Topology.Inseparable
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 81 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.imageproof · cited by 5,609
- IsOpenproof · cited by 2,400
- le_antisymmproof · cited by 2,068
- Topology.IsInducingstatement · cited by 266
- SeparationQuotientstatement · cited by 128
- SeparationQuotient.mkstatement and proof · cited by 94
- continuous_iff_le_inducedproof · cited by 16
- SeparationQuotient.continuous_mkproof · cited by 9
- SeparationQuotient.isOpenMap_mkproof · cited by 5
- SeparationQuotient.preimage_image_mk_openproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- SeparationQuotient.comap_mk_nhdsSet_imageproof · cited by 2
- SeparationQuotient.comap_mk_nhds_mkproof · cited by 2
- LocallyCompactSpace.of_finiteDimensional_of_completeproof · cited by 1
- SeparationQuotient.isClosedMap_mkproof · cited by 1
- SeparationQuotient.exists_out_continuousLinearMapproof · cited by 1
- continuous_congr_of_inseparableproof · cited by 1
- SeparationQuotient.t1Space_iffproof · cited by 0