Certain continua in 𝑆ⁿ of the same shape have homeomorphic complements

Author:

Liem Vo Thanh

Abstract

As a consequence of Theorem 1 of this paper, we see that if X and Y are globally 1-alg continua in S n ( n 5 ) {S^n}\;(n \geqslant 5) having the shape of the real projective space P k ( k 2 , 2 k + 2 n ) {P^k}\;(k \ne 2,2k + 2 \leqslant n) , then S n X S n Y {S^n} - X \approx {S^n} - Y . (For P 1 = S 1 {P^1} = {S^1} , this establishes the last case of such a result for spheres.) We also show that if X and Y are globally 1-alg continua in S n , n 6 {S^n},n \geqslant 6 , which have the shape of a codimension 3 \geqslant 3 , closed, 0 > ( 2 m n + 1 ) 0 > (2m - n + 1) -connected, PL-manifold M m {M^m} , then S n X S n Y {S^n} - X \approx {S^n} - Y .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference22 articles.

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4. Shapes of finite-dimensional compacta;Chapman, T. A.;Fund. Math.,1972

5. D. Coram, R. J. Daverman, and P. F. Duvall, Jr., A small loop condition for embedded compacta, Trans. Amer. Math. Soc. (to appear).

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Weak flatness for shape classes of sphere-like continua;General Topology and its Applications;1977

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