Mathlib Map

Theorems · Theorem · general topology

TopologicalSpace.ext_nhds

∀ {X : Type u_2} {t t' : TopologicalSpace X}, (∀ (x : X), nhds x = nhds x) → t = t'

Alias of the reverse direction of TopologicalSpace.ext_iff_nhds.

Defined in
Mathlib.Topology.Neighborhoods
Cited by
10 results in Mathlib
Foundations
Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

UniformSpace.ext · cited by 34UniformSpace.extUniformSpace.toTopologicalSpace_iInf · cited by 6UniformSpace.toTopologica…TopologicalSpace.IsTopologicalBasis.of_hasBasis_nhds · cited by 6IsTopologicalBasis.of_has…IsTopologicalAddGroup.ext · cited by 4IsTopologicalAddGroup.extIsTopologicalGroup.ext · cited by 1IsTopologicalGroup.extIndiscreteTopology.of_forall_inseparable · cited by 1IndiscreteTopology.of_for…Ctop.Realizer.ext' · cited by 1Realizer.ext'UniformSpace.toCore_toTopologicalSpace · cited by 0UniformSpace.toCore_toTop…orderTopology_of_nhds_abs · cited by 0orderTopology_of_nhds_absorderTopology_of_nhds_mabs · cited by 0orderTopology_of_nhds_mabsTopologicalSpace · cited by 24529TopologicalSpaceFilter · cited by 8121Filternhds · cited by 5554nhdsTopologicalSpace.ext_iff_nhds · cited by 1TopologicalSpace.ext_iff_…TopologicalSpace.ext_nhdsCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by10

Results whose statement or proof uses this declaration.