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Theorems · Theorem · general topology

Path.continuous_extend

∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X} (γ : Path x y), Continuous ⇑γ.extend

A useful special case of Continuous.path_extend.

Defined in
Mathlib.Topology.Path
Cited by
1 results in Mathlib
Foundations
Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Path.truncate_continuous_family · cited by 1Path.truncate_continuous_…DFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealTopologicalSpace · cited by 24529TopologicalSpaceContinuous · cited by 2592ContinuousContinuousMap · cited by 2491ContinuousMapPath · cited by 318PathPath.extend · cited by 52Path.extendPath.continuous · cited by 3Path.continuousContinuous.Icc_extend' · cited by 3Continuous.Icc_extend'Path.continuous_extendCITED BYCITES

Cites9

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Cited by1

Results whose statement or proof uses this declaration.