Theorems · Theorem · general topology
nhdsSet_mono
∀ {X : Type u_2} [inst : TopologicalSpace X] {s t : Set X}, s ⊆ t → nhdsSet s ≤ nhdsSet t- Defined in
- Mathlib.Topology.NhdsSet
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsSetstatement · cited by 267
- Set.image_monoproof · cited by 197
- sSup_le_sSupproof · cited by 24
Cited by18
Results whose statement or proof uses this declaration.
- monotone_nhdsSetproof · cited by 5
- Iio_mem_nhdsSet_Iccproof · cited by 4
- nhdsKer_monoproof · cited by 4
- Ioi_mem_nhdsSet_Iccproof · cited by 4
- Iio_mem_nhdsSet_Icoproof · cited by 3
- Ioi_mem_nhdsSet_Iocproof · cited by 3
- Iic_mem_nhdsSet_Iocproof · cited by 2
- Iio_mem_nhdsSet_Iocproof · cited by 2
- Ioi_mem_nhdsSet_Icoproof · cited by 2
- nhdsSet_nhdsKerproof · cited by 2
- Ici_mem_nhdsSet_Icoproof · cited by 2
- IsClosed.nhdsSet_le_supproof · cited by 1