On Generalized Manifolds
Solomon Lefschetz · Birkhäuser Basel eBooks · 1993
The object of the present paper is to extend to a larger class of spaces certain results recently obtained for topological manifolds. † The extension consists in replacing the requirement that every point possess a combinatorial cell for neighborhood by certain weaker conditions on the chains through the point. Eoughly speaking they amount to demanding that locally any p -chain be deformable (in a certain very general sense) into one’which does not meet any assigned q -space (= q dimensional space), where p + q < n , the dimension of the manifold. This extension is made in Part III of the present paper. In Part I we take up again, partly as a preparation to the second Part, the homology theory of metric spaces from the standpoint initiated in our Colloquium Lectures Topology , Ch. VII. The notation and terminology are as in our book. ‡ These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.