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Locally nice codimension one manifolds are locally flat. (English) Zbl 0256.57005


MSC:

57N45 Flatness and tameness of topological manifolds
57N35 Embeddings and immersions in topological manifolds
57N50 \(S^{n-1}\subset E^n\), Schoenflies problem
57N15 Topology of the Euclidean \(n\)-space, \(n\)-manifolds (\(4 \leq n \leq \infty\)) (MSC2010)
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References:

[1] W.-c. Hsiang and C. T. C. Wall, On homotopy tori. II, Bull. London Math. Soc. 1 (1969), 341 – 342. · Zbl 0181.27101
[2] Robion C. Kirby, Stable homeomorphisms and the annulus conjecture, Ann. of Math. (2) 89 (1969), 575 – 582. · Zbl 0176.22004
[3] R. C. Kirby and L. C. Siebenmann, On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc. 75 (1969), 742 – 749. · Zbl 0189.54701
[4] T. M. Price and C. L. Seebeck III, Approximations of somewhere nice codimension one manifolds having 1-ULC complements. I (to appear). · Zbl 0297.57009
[5] T. M. Price and C. L. Seebeck III, Approximations of somewhere nice codimension one manifolds having l-ULC complements. II (to appear). · Zbl 0297.57009
[6] T. B. Rushing, Infinite engulfing (to appear). · Zbl 0246.57007
[7] C. L. Seebeck III, Collaring and (\?-1)-manifold in an \?-manifold, Trans. Amer. Math. Soc. 148 (1970), 63 – 68. · Zbl 0194.55702
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