annulus conjecture

annulus conjecture

[′an·yə·ləs kən′jek·chər]

(mathematics)

For dimension n, the assertion that if f and g are locally flat embeddings of the (n- 1) sphere, S ^{n- 1}, in real n space, Rⁿ, with f (S ^{n- 1}) in the bounded component of Rⁿ-g (S ^{n- 1}), then the closed region in Rⁿ bounded by f (S ^{n- 1}) and g (S ^{n- 1}) is homeomorphic to the direct product of S ^{n- 1}and the closed interval [0,1]; it is established for n ≠ 4.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.