Theorems · Theorem · general topology
continuous_inclusion
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X} (h : s ⊆ t), Continuous (Set.inclusion h)- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 73 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.
Cites7
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
- Continuousstatement · cited by 2,592
- continuous_idproof · cited by 192
- Set.inclusionstatement · cited by 145
- Continuous.subtype_mapproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- ContinuousMap.concat_comp_IccInclusionLeftproof · cited by 2
- ContinuousMap.concat_comp_IccInclusionRightproof · cited by 2
- ContinuousMap.inclusionproof · cited by 2
- connectedComponentIn_monoproof · cited by 2
- Pi.continuous_domRestrict₂_applyproof · cited by 1
- IsDenseInducing.isUniformInducing_extendproof · cited by 1
- Finset.continuous_restrict₂_applyproof · cited by 0
- intrinsicClosure_monoproof · cited by 0
- isClosedEmbedding_cfcₙHom_of_cfcHomproof · cited by 0