Theorems · Theorem · general topology
IsOpen.isOpenMap_inclusion
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, IsOpen s → ∀ (h : s ⊆ t), IsOpenMap (Set.inclusion h)- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Set.Elemstatement · cited by 7,166
- IsOpenstatement and proof · cited by 2,400
- IsOpenMapstatement · cited by 253
- Set.inclusionstatement · cited by 145
- IsOpenMap.idproof · cited by 12
- IsOpenMap.subtype_mapproof · cited by 1
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