Abstract
This paper gives a generalization of smoothing theorems for finitedifferentiable manifolds. Every finite-differentiable space, i.e. manifold with arbitrary singularities, can be smoothed to an infinitedifferentiable space having the same embedding dimension at each point. So our theorem improves a result of Spallek [6] on smoothings in a way which one needs for various types of applications (see for examole [2]). Finally a counterexample is given that in contrast to manifolds smoothings even for nice spaces are in general not unique.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literatur
Breuer, M.; Marshall, Ch. D.: Banachian differentiable spaces Math. Ann. 237, 105–120 (1978)
Kiesow, N.: Einbettungen von Räumen in Mannigfaltigkeiten minimaler Dimension Dissertation, Bochum 1979
Munkres, J.: Elementary Differential Topology Revised edition, Princeton, New Yersey, Princeton University Press, 1966
Schafmeister, O.: Differenzierbare Räume Forschungsbericht des Landes Nordrhein-Westfalen, Nr. 2140, Westdeutscher Verlag, Köln und Opladen 1970
Spallek, K.: Differenzierbare Räume Math. Ann. 180, 269–296 (1969)
Spallek, K.: Glättung differenzierbarer Räume Math. Ann. 186, 233–248 (1970)
Teufel, M.: Differenzierbare Strukturen und Jetbündel auf Räumen mit Singularitäten Dissertation, Bochum 1979
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Teufel, M. Glättung endlich-differenzierbarer Räume. Manuscripta Math 33, 37–49 (1980). https://doi.org/10.1007/BF01298336
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01298336