Abstract and Applied Analysis
Volume 2006 (2006), Article ID 82602, 9 pages
doi:10.1155/AAA/2006/82602
Theorem on the union of two topologically flat cells of codimension 1 in ℝn
Institute of the Information Transmission Problems, Russian Academy of Sciences, Bolshoy Karetny per. 19, Moscow 117 447, Russia
Received 26 June 2005; Accepted 1 July 2005
Copyright © 2006 A. V. Chernavsky. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper we give a complete and improved proof of the “Theorem on the union of two (n−1)-cells.” First time it was proved by the author in the form of reduction to the earlier
author's technique. Then the same reduction by the same method was
carried out by Kirby. The proof presented here gives a more clear
reduction. We also present here the exposition of this technique
in application to the given task. Besides, we use a modification
of the method, connected with cyclic ramified coverings, that
allows us to bypass referring to the engulfing lemma as well as to
other multidimensional results, and so the theorem is proved also
for spaces of any dimension. Thus, our exposition is complete and
does not require references to other works for the needed technique.