Theorems · Theorem · general topology
ConnectedComponents.surjective_coe
∀ {α : Type u} [inst : TopologicalSpace α], Function.Surjective ConnectedComponents.mk- Defined in
- Mathlib.Topology.Connected.Clopen
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- ConnectedComponentsstatement · cited by 40
- Quot.mk_surjectiveproof · cited by 34
- ConnectedComponents.mkstatement · cited by 25
Cited by8
Results whose statement or proof uses this declaration.
- connectedComponents_lift_unique'proof · cited by 1
- IsOpenMap.enatCard_connectedComponents_le_encard_preimage_singletonproof · cited by 1
- ConnectedComponents.nonempty_iff_nonemptyproof · cited by 1
- Continuous.connectedComponentsMap_surjectiveproof · cited by 1
- ConnectedComponents.discreteTopology_iffproof · cited by 0
- Topology.IsCoinducing.connectedComponentsMap_bijectiveproof · cited by 0
- ConnectedComponents.range_coeproof · cited by 0
- IsOpenMap.finite_connectedComponents_of_finite_preimage_singletonproof · cited by 0