Theorems · Theorem · general topology
nhds_discrete
∀ (α : Type u_3) [inst : TopologicalSpace α] [DiscreteTopology α], nhds = pure
- Defined in
- Mathlib.Topology.Order
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- le_antisymmproof · cited by 2,068
- IsOpen.mem_nhdsproof · cited by 470
- DiscreteTopologystatement and proof · cited by 373
- pure_le_nhdsproof · cited by 39
- isOpen_discreteproof · cited by 36
Cited by23
Results whose statement or proof uses this declaration.
- IsCompact.finite_of_discreteproof · cited by 4
- NormedRing.inverse_addproof · cited by 2
- singleton_mem_nhdsWithin_of_mem_discreteproof · cited by 2
- IsLindelof.countable_of_discreteproof · cited by 2
- ENat.nhds_natCastproof · cited by 1
- Subgroup.discreteTopology_iff_of_finiteIndexproof · cited by 1
- MvPowerSeries.coeff_zero_iffproof · cited by 1
- WithTop.tendsto_coe_atTopproof · cited by 1
- WithTop.tendsto_nhds_top_iffproof · cited by 1
- AddSubgroup.discreteTopology_iff_of_finiteIndexproof · cited by 1
- OnePoint.not_continuous_cofiniteTopology_of_symmproof · cited by 1
- continuousWithinAt_prod_of_discrete_leftproof · cited by 1