Functors of finite degree in the asymptotic category

Authors

  • Михайло Михайлович Зарічний Lviv National University, Ukraine
  • Михайло Миколайович Романський Drohobych State Pedagogical University, Ukraine
  • Олекcандр Григорович Савченко Kherson State Agrarian University, Ukraine

DOI:

https://doi.org/10.15673/2072-9812.1/2015.50167

Keywords:

Asymptotic category, functor, symmetric power, projective power

Abstract

We consider functors in the asymptotic category generated by some functors of finite degree in the category of compacta. Some geometric properties of these functors are established.

Author Biographies

Михайло Михайлович Зарічний, Lviv National University

Department of Mechanics and Mathematics, Dean

Михайло Миколайович Романський, Drohobych State Pedagogical University

PhD student

Олекcандр Григорович Савченко, Kherson State Agrarian University

Department of Economics, Dean

References

М.М. Заричный, Фундаментальная группа суперрасширения lambda_n(X). В кн.: Отображения и функторы. Под ред. П.С. Александрова. --- Москва: МГУ,1984 - С. 24-31.

В.В. Федорчук, В.В. Филиппов, Общая топология. Основные конструкции. - -- М. -- 2006.

R. Bott, On The Third Symmetric Potency of S_1. Fund. Math. 39(1952), 264--268.

C. H. Wagner, Symmetric, cyclic, and permutation products of manifolds.- Rozprawy Matematyczne tom/nr w serii: 182. wydano: 1980

A. Dranishnikov, Asymptotic topology. - Russian Math. Surveys., Vol. 55, No 6 (2000), P. 71-116.

A. Dranishnikov, M. Zarichnyi, Universal spaces for asymptotic dimension. - Topol. Appl., Vol. 140, No 2-3 (2004), P. 203-225.

I. Protasov, M. Zarichnyi, General asymptology. - (Math. Studies: Monograph Series. - Vol. XII) Lviv: VNTL Publ, (2007), 219 P.

A. Teleiko, M. Zarichnyi, Categorical topology of compact Hausdorff spaces. - Mathematical Studies Monograph Series, 5. VNTL Publishers, Lviv, 1999. 256 pp.

O. Shukel', Functors of finite degree and asymptotic dimension zero. -Mat. Stud. 29(2008), No 1, 101--107.

J. Mostovoy, Lattices in C and finite subsets of a circle. - Amer. Math. Monthly 111(4): 357-360 (2004)

A. Szankowski, Projective potencies and multiplicative extension operators. - Fundamenta Mathematicae (1970) Volume: 67, Issue: 1, 97--113.

A. Dold, R. Thom, Quasifaserungen und unendliche symmetrische Produkte. - Annals of Mathematics. Second Series 67(1958), 239–-281

Published

2015-09-14