Theorem on the union of two topologically flat cells of codimension 1 in ℝn
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 g...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA/2006/82602 |
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| author | A. V. Chernavsky |
| author_facet | A. V. Chernavsky |
| author_sort | A. V. Chernavsky |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e339dcd705674025a5074c7a0d4b4854 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e339dcd705674025a5074c7a0d4b48542025-02-03T05:47:07ZengWileyAbstract and Applied Analysis1085-33751687-04092006-01-01200610.1155/AAA/2006/8260282602Theorem on the union of two topologically flat cells of codimension 1 in ℝnA. V. Chernavsky0Institute of the Information Transmission Problems, Russian Academy of Sciences, Bolshoy Karetny per. 19, Moscow 117 447, RussiaIn 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.http://dx.doi.org/10.1155/AAA/2006/82602 |
| spellingShingle | A. V. Chernavsky Theorem on the union of two topologically flat cells of codimension 1 in ℝn Abstract and Applied Analysis |
| title | Theorem on the union of two topologically flat cells of codimension 1 in ℝn |
| title_full | Theorem on the union of two topologically flat cells of codimension 1 in ℝn |
| title_fullStr | Theorem on the union of two topologically flat cells of codimension 1 in ℝn |
| title_full_unstemmed | Theorem on the union of two topologically flat cells of codimension 1 in ℝn |
| title_short | Theorem on the union of two topologically flat cells of codimension 1 in ℝn |
| title_sort | theorem on the union of two topologically flat cells of codimension 1 in rn |
| url | http://dx.doi.org/10.1155/AAA/2006/82602 |
| work_keys_str_mv | AT avchernavsky theoremontheunionoftwotopologicallyflatcellsofcodimension1inrn |