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Theorems · Theorem · algebraic topology

IsSimplyConnected.nonempty

∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X}, IsSimplyConnected s → s.Nonempty
Defined in
Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected
Cited by
1 results in Mathlib
Foundations
Depth 143 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.

Complex.exists_continuousOn_eqOn_exp_comp · cited by 1Complex.exists_continuous…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.Nonempty · cited by 2627Set.NonemptyIsSimplyConnected · cited by 13IsSimplyConnectedIsPathConnected.nonempty · cited by 2IsPathConnected.nonemptyIsSimplyConnected.isPathConnected · cited by 1IsSimplyConnected.isPathC…IsSimplyConnected.nonemptyCITED BYCITES

Cites6

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Cited by1

Results whose statement or proof uses this declaration.