Sticky arcs in 𝐸ⁿ (𝑛≥4)

Author:

Wright David G.

Abstract

Let A and B be arcs in E 3 {E^3} , Euclidean 3-space. Then A can be “slipped” off B; i.e., there exists a homeomorphism of E 3 {E^3} onto itself, arbitrarily close to the identity, such that h ( A ) B = h(A) \cap B = \emptyset . The purpose of this note is to show that arcs in E n ( n 4 ) {E^n}(n \geqslant 4) do not always enjoy this property. The examples depend heavily on a recent result of McMillan.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference6 articles.

1. Decompostions of 𝐸³ with a compact 𝑂-dimensional set of nondegenerate elements;Armentrout, Steve;Trans. Amer. Math. Soc.,1966

2. A reduction of the Schoenflies extension problem;Morse, Marston;Bull. Amer. Math. Soc.,1960

3. Deformations of spaces of imbeddings;Edwards, Robert D.;Ann. of Math. (2),1971

4. An arc in a 𝑃𝐿 𝑛-manifold with no neighborhood that embeds in 𝑆ⁿ,𝑛≥4;McMillan, D. R., Jr.;Michigan Math. J.,1978

5. A criterion for cellularity in a manifold. II;McMillan, D. R., Jr.;Trans. Amer. Math. Soc.,1967

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