Point sets in three and higher dimensions and their investigation by means of a unified analysis situs

Abstract

It might seem that in the case of Lefschetz' Colloquium, this remark is not true, since he considers topics that are ordinarily considered as part of the set-theoretic topology, for example, compact metric spaces. However, as we shall show, it is in method, not subject matter, that the two schools of topology differ, and in this sense Lefschetz' book is combinatorial. * Loc. cit. * Loc. cit. t That is, the converse of the Jordan-Brouwer separation theorem in E 3 (see Kline, loc. cit.,, and the finding of necessary and sufficient conditions that the sum of two closed connected sets, neither of which separates E 3 , may have