Classification_of_Compact_One_Manifolds

⚠️ Retired — incorrect formalization

The Lean statement below does not express the result Classification_of_Compact_One_Manifolds is named for, so its Proved status carries no information about it. Do not import it or use it as a dependency.

Every compact one-dimensional manifold is diffeomorphic to either a circle or a closed interval.

Why this node was retired

The posted statement is

import Mathlib.Analysis.Complex.Basic
import Mathlib.Topology.Basic

theorem Classification_of_Compact_One_Manifolds : ∀ (M : Type _) [TopologicalSpace M] [CompactSpace M] [ConnectedSpace M], True := by sorry

The goal is ∀ (M : Type _) [TopologicalSpace M] [CompactSpace M] [ConnectedSpace M], True, which is closed by fun _ _ _ _ => trivial. No manifold structure is imposed and no classification is asserted.

What a faithful statement would require

The statement must impose a genuine one-dimensional manifold structure (with or without boundary) and conclude homeomorphism with a circle or a closed interval.

No corrected replacement node exists yet.