$M$-equivalence of mappings

N.M.Pyrch

The paper investigates the relation of $M$-equivalence of mappings. We present functors preserving this relation. A new method for constructing examples of $M$-equivalent mappings is given and, as a corollary, we obtain a list of properties of mappings which are not preserved by $M$-equivalence. Some characterizations of $M$-equivalence of spaces in terms of $M$-equivalence of mappings are presented. A complete classification of $A$-equivalent mappings having right inverse up to $A$-equivalent spaces is given.

1. Guran I. Y., Zarichnyi M. M. Elements of theory of topological groups, Inst. System Stud. Education, Kyiv, 1991.

2. Энгелькинг Р. Общая топология, М.: Мир, 1986.

3. Yunusov A. S. On quasicomponent of free topological groups, Mat. Issledovania 74 (1983), Kishinev, 163--165. (Russian)

4. Куратовский К. Топология, М.: Мир. Т.1. 1966, Т.2. 1969.

5. Okunev O. G. A method for consructing examples of M-equivalent spaces, Topology Appl 36 (1990), 157--171; Correction, Topology Appl 49 (1993), 191--192.

6. Okunev O. G. M-equivalence of products, Trudy Mosc. Math. Obsch. 56 (1995), 192--205.

7. Pestov V. G. Universal arrows to forgetful functors from categories of topological algebra, Bull. Austr. Math. Soc. 48 (1993), 209--249.

8. Pyrch N. M. Orthogonal retractions and the relations of M-equivalence, Matematychni Studii, 20, No.~2 (2003), 151--161.

9. Pyrch N., Zarichnyi M. On a generalization of Okunev's construction, Algebraic structures and their applications, Proceedings of the Institute of Math.: Kiev, 2002, 346--350.

10. Sipacheva O. V. Free topological groups of spaces and their subspaces, Topology Appl., 101 (2000), 181--212.

11. Tkachenko M. G. On the competeness of free Abelian topological groups, Dokl. Akad. Nauk SSSR 269 (1983), 299--303. (Russian)

12. Ткачук В. В. Об одном методе построения $M$-эквивалентных пространств, Усп. матем. наук, 38 (1983), № 6, 127--128.

13. Wagner C. H. Symmetric, cyclic and permutation products of manifolds, Dissertationes mathematicae, CLXXXII, Warszawa, 1980.

	$M$-equivalence of mappings
Author	N.M.Pyrch Ivan Franko National University of Lviv
Abstract	The paper investigates the relation of $M$-equivalence of mappings. We present functors preserving this relation. A new method for constructing examples of $M$-equivalent mappings is given and, as a corollary, we obtain a list of properties of mappings which are not preserved by $M$-equivalence. Some characterizations of $M$-equivalence of spaces in terms of $M$-equivalence of mappings are presented. A complete classification of $A$-equivalent mappings having right inverse up to $A$-equivalent spaces is given.
Keywords	M-equivalent mapping, functor, A-equivalent mapping
DOI	doi:10.30970/ms.24.1.21-30
Reference	1. Guran I. Y., Zarichnyi M. M. Elements of theory of topological groups, Inst. System Stud. Education, Kyiv, 1991. 2. Энгелькинг Р. Общая топология, М.: Мир, 1986. 3. Yunusov A. S. On quasicomponent of free topological groups, Mat. Issledovania 74 (1983), Kishinev, 163--165. (Russian) 4. Куратовский К. Топология, М.: Мир. Т.1. 1966, Т.2. 1969. 5. Okunev O. G. A method for consructing examples of M-equivalent spaces, Topology Appl 36 (1990), 157--171; Correction, Topology Appl 49 (1993), 191--192. 6. Okunev O. G. M-equivalence of products, Trudy Mosc. Math. Obsch. 56 (1995), 192--205. 7. Pestov V. G. Universal arrows to forgetful functors from categories of topological algebra, Bull. Austr. Math. Soc. 48 (1993), 209--249. 8. Pyrch N. M. Orthogonal retractions and the relations of M-equivalence, Matematychni Studii, 20, No.~2 (2003), 151--161. 9. Pyrch N., Zarichnyi M. On a generalization of Okunev's construction, Algebraic structures and their applications, Proceedings of the Institute of Math.: Kiev, 2002, 346--350. 10. Sipacheva O. V. Free topological groups of spaces and their subspaces, Topology Appl., 101 (2000), 181--212. 11. Tkachenko M. G. On the competeness of free Abelian topological groups, Dokl. Akad. Nauk SSSR 269 (1983), 299--303. (Russian) 12. Ткачук В. В. Об одном методе построения $M$-эквивалентных пространств, Усп. матем. наук, 38 (1983), № 6, 127--128. 13. Wagner C. H. Symmetric, cyclic and permutation products of manifolds, Dissertationes mathematicae, CLXXXII, Warszawa, 1980.
Pages	21-30
Volume	24
Issue	1
Year	2005
Journal	Matematychni Studii
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