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Mathematical Communications, Vol.13 No.2 December 2008. -

We present two classical conjectures concerning the characterization

of manifolds: the Bing Borsuk conjecture asserts that every

n-dimensional homogeneous ANR is a topological n-manifold,

whereas the Busemann conjecture asserts that every n-dimensional

G-space is a topological n-manifold. The key object in both

cases are so-called i.e. ENR homology manifolds. We look at the history from the early beginnings to the present day. We also list several open problems and related conjectures.

Bing-Borsuk conjecture; homogeneity; ANR; Busemann G-space; Busemann conjecture; Moore conjecture; de Groot conjecture; generalized manifold; cell-like resolution; general position property; delta embedding property; disjoint disks property; recognition

Author: Denise M. Halverson - ; Department of Mathematics, Brigham Young University,Provo, U.S.A. Dušan Repovš - ; Faculty of Mathemati



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