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Theorems · Definition · general topology

TotallyDisconnectedSpace.continuousMapEquivOfConnectedSpace

(X : Type u_3) →
  (Y : Type u_4) →
    [inst : TopologicalSpace X] →
      [inst_1 : TopologicalSpace Y] → [TotallyDisconnectedSpace Y] → [ConnectedSpace X] → C(X, Y) ≃ Y

The bijection C(X, Y) ≃ Y when Y is totally disconnected and X is connected.

Defined in
Mathlib.Topology.Connected.TotallyDisconnected
Cited by
1 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceTotallyDisconnectedSpaceConnectedSpace
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Around this declaration

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TotallyDisconnectedSpace.continuousMapEquivOfConnectedSpace_symm_apply_apply · cited by 0TotallyDisconnectedSpace.…TopCat.toSSetIsoConst · cited by 0TopCat.toSSetIsoConstDFunLike.coe · cited by 62936DFunLike.coeTopologicalSpace · cited by 24529TopologicalSpaceEquiv · cited by 8337EquivContinuousMap · cited by 2491ContinuousMapTotallyDisconnectedSpace · cited by 295TotallyDisconnectedSpaceClassical.arbitrary · cited by 161Classical.arbitraryConnectedSpace · cited by 37ConnectedSpaceTotallyDisconnectedSpace.cont…CITED BYCITES

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