Theorems · Theorem · general topology
nhds_iInf
∀ {α : Type u} {ι : Sort u_1} {t : ι → TopologicalSpace α} {a : α}, nhds a = ⨅ i, nhds a- Defined in
- Mathlib.Topology.Order
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- iInfstatement · cited by 1,690
- GaloisConnection.u_iInfproof · cited by 40
- gc_nhdsproof · cited by 8
Cited by14
Results whose statement or proof uses this declaration.
- nhds_piproof · cited by 29
- UniformSpace.toTopologicalSpace_iInfproof · cited by 6
- SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInfproof · cited by 3
- equicontinuousWithinAt_iInf_domproof · cited by 2
- EquicontinuousOn.tendsto_uniformOnFun_iff_pi'proof · cited by 2
- LinearMap.mem_span_iff_continuousproof · cited by 1
- IsTopologicalBasis.iInfproof · cited by 1
- ContinuousMap.tendsto_compactOpen_iff_forallproof · cited by 1
- SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInfproof · cited by 1
- completelyRegularSpace_iInfproof · cited by 1
- LinearMap.mem_span_iff_continuous_of_finiteproof · cited by 0
- equicontinuousWithinAt_iInf_rngproof · cited by 0