Theorems · Theorem · algebraic topology

Topology.IsEmbedding.isSimplyConnected_image

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
  Topology.IsEmbedding f → ∀ {s : Set X}, IsSimplyConnected (f '' s) ↔ IsSimplyConnected s

Defined in: Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected
Cited by: 1 results in Mathlib
Foundations: Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace

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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.imagestatement · cited by 5,609
Topology.IsEmbeddingstatement and proof · cited by 294
IsSimplyConnectedstatement · cited by 13
Homeomorph.toHomotopyEquivproof · cited by 7
Topology.IsEmbedding.homeomorphImageproof · cited by 3
ContinuousMap.HomotopyEquiv.simplyConnectedSpace_iffproof · cited by 1

Cited by1

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Homeomorph.isSimplyConnected_imageproof · cited by 3