Showing papers on "Effective dimension published in 1974"
TL;DR: This paper constructs for each n>=3, k>=0, a poset, called a crown and denoted S^k"n, for which the dimension is given by the formula [email protected]?(n+k)(k+2).
42 citations
39 citations
25 citations
TL;DR: In this article, a complete shape classification for F -like Hausdorff continua, F n. like H-continua, and S n -like continua is obtained.
Abstract: Let F be the collection of finite dimensional tori, F n the tori of dimension n or less, and S n the n -sphere. A complete shape classification for F -like Hausdorff continua, F n . like Hausdorff continua, and S n -like Hausdorff continua is obtained. If M is a F -like continuum, then there exists a unique compact connected abelian group having the same shape as M . If M is an S n -like Hausdorff continuum, then there exists a unique compact connected abelian group G M of dimension 1 or less such that the ( n −1)-fold suspension of G M has the same shape as M . As a consequence of these results, every F n -like Hausdorff continuum and every S n -like Hausdorff continuum has the shape of a metric continuum.
7 citations