Theorems · Theorem · general topology
ConnectedComponents.continuous_coe
∀ {α : Type u} [inst : TopologicalSpace α], Continuous ConnectedComponents.mk- Defined in
- Mathlib.Topology.Connected.Clopen
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 68 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement · cited by 2,592
- ConnectedComponentsstatement · cited by 40
- ConnectedComponents.mkstatement · cited by 25
- Topology.IsQuotientMap.continuousproof · cited by 14
- ConnectedComponents.isQuotientMap_coeproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- IsOpenMap.enatCard_connectedComponents_le_encard_preimage_singletonproof · cited by 1
- Continuous.connectedComponentsMap_continuousproof · cited by 0
- IsOpenMap.finite_connectedComponents_of_finite_preimage_singletonproof · cited by 0