Scientific Papers of the College of Arts and Sciences, The University of Tokyo. Vol.41(1991), Page59-81
We assume that there is given a locally finite family of euclidean subspaces in a euclidean space. In this paper we construct a locally finite regular cell complex which is simple homotopy equivalent to the complement of the union of the subspaces in question. The construction is done by generalizing the one employed by Deligne in the case when every member of the family is a real hyperplane in C$F^n$.