Vol. 60, No. 2, 1975

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ISSN: 0030-8730
Embeddings of shape classes of compacta in the trivial range

John G. Hollingsworth and Thomas Benny Rushing

Vol. 60 (1975), No. 2, 103–110
Abstract

We show that for compacta X,Y Rn, n 5, satisfying the small loops condition and having dimensions in the trivial range with respect to n, Sh(X) = Sh(Y ) if and only if Rn X Rn Y . As a corollary we obtain the following result whose statement is void of shape: If X,Y Rn, n 5, are homeomorphic compacta satisfying the small loops condition and having dimensions in the trivial range with respect to n, then Rn X Rn Y .

Mathematical Subject Classification 2000
Primary: 57A40
Secondary: 54C56
Milestones
Received: 14 April 1975
Revised: 18 July 1975
Published: 1 October 1975
Authors
John G. Hollingsworth
Thomas Benny Rushing