Theorems · Theorem · general topology
Filter.inter_sets
∀ {α : Type u_1} (self : Filter α) {x y : Set α}, x ∈ self.sets → y ∈ self.sets → x ∩ y ∈ self.setsIf two sets belong to a filter, then their intersection belongs to the filter as well.
- Defined in
- Mathlib.Order.Filter.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Filter.setsstatement · cited by 56
Cited by4
Results whose statement or proof uses this declaration.
- Filter.inter_memproof · cited by 153
- symmetrize_mem_uniformityproof · cited by 11
- UniformSpace.hasBasis_nhds_prodproof · cited by 1
- nhds_of_nhdsWithin_of_nhdsproof · cited by 0