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The aim of this paper is to introduce the sublinear Higson corona and showthat the sublinear Higson corona of Euclidean cone of P and X is decomposedinto the product of P and that of X. Here P is a compact metric space and X isunbounded proper metric space. For example, the sublinear Higson corona ofn-dimensional Euclidean space is homeomorphic to the product of(n-1)-dimensional sphere and that of natural numbers.

Sublinear Higson corornae of Euclidean cones