A uniform generalized Schoenflies theorem

Wright, Perrin

doi:10.1090/s0002-9904-1968-12011-7

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Preliminary Results Our Proof Depends Heavily Upon the Foll1

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1970

1976

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Cited by 3 publications

(2 citation statements)

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“…Outline of Proof. The proof is implicit in Wright's proof in [10]. From the remarks following Lemma 1 it is sufficient to show that h can be extended to such that H0=h0, Hx = hy, and diam H(xxI)<s for each xe M. H is constructed roughly as follows: Using a sequence of small engulfings move collars on h0(M) and hx(M) so that the whole collars are very close.…”

Section: Preliminary Results Our Proof Depends Heavily Upon the Follmentioning

confidence: 99%

Collaring and $(n-1)$-manifold in an $n$-manifold

Seebeck¹

1970

Trans. Amer. Math. Soc.

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Section: Preliminary Results Our Proof Depends Heavily Upon the Follmentioning

confidence: 99%

Collaring and $(n-1)$-manifold in an $n$-manifold

Seebeck¹

1970

Trans. Amer. Math. Soc.

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“…It follows from [18] (see also [16 To verify that XtcN, observe that TV has connected boundary, as does Xt (where Bd Xt is taken in En + 1, not in Cl U). Since Bd Xt^N by construction and since both Xt and TV are bounded, Xt must be a subset of TV.…”

mentioning

confidence: 95%

Slicing theorems for 𝑛-spheres in Euclidean (𝑛+1)-space

Daverman¹

1972

Trans. Amer. Math. Soc.

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Abstract. This paper describes conditions on the intersection of an «-sphere 2 in Euclidean (n+l)-space En + 1 with the horizontal hyperplanes of En + 1 sufficient to determine that the sphere be nicely embedded. The results generally are pointed towards showing that the complement of 2 is 1-ULC (uniformly locally 1-connected) rather than towards establishing the stronger property that S is locally flat. For instance, the main theorem indicates that £" + 1-S is 1-ULC provided each nondegenerate intersection of S and a horizontal hyperplane be an (»-l)-sphere bicollared both in that hyperplane and in S itself («^4).

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Some new engulfing theorems

Crary¹

1976

Pacific J. Math.

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A uniform generalized Schoenflies theorem

Cited by 3 publications

References 6 publications

Collaring and $(n-1)$-manifold in an $n$-manifold

Collaring and $(n-1)$-manifold in an $n$-manifold

Slicing theorems for 𝑛-spheres in Euclidean (𝑛+1)-space

Some new engulfing theorems

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