Theorems · Theorem · general topology
Filter.principal_empty
∀ {α : Type u}, Filter.principal ∅ = ⊥- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, 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.
- Setstatement and proof · cited by 53,352
- Filterstatement · cited by 8,121
- Bot.botstatement and proof · cited by 4,720
- Filter.principalstatement · cited by 740
- Set.empty_subsetproof · cited by 70
- bot_uniqueproof · cited by 57
Cited by20
Results whose statement or proof uses this declaration.
- nhdsWithin_emptyproof · cited by 16
- Filter.self_mem_codiscreteWithinproof · cited by 7
- nhdsSet_emptyproof · cited by 7
- Filter.lift'_botproof · cited by 3
- Filter.Realizer.botproof · cited by 3
- HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principalproof · cited by 3
- hasFDerivWithinAt_singletonproof · cited by 2
- BoundedVariationOn.exists_tendsto_atTopproof · cited by 2
- boundary_principalproof · cited by 1
- OnePoint.comap_coe_nhds_inftyproof · cited by 1
- Filter.map_inl_inf_map_inrproof · cited by 1
- MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurableproof · cited by 1