Problems on absorbing sets in the hyperspace theory and the theory of
functions

Bazylevych L., Tkach O., Zarichnyi M.

The method of absorbing sets, which has its origin in the works of Anderson, Bessaga and Pełczyński, is now one of the most powerful tools of infinite-dimensioanl topology having numerous applications not only in topology but also in other areas of mathematics. In its modern form, the method of absorbing sets is developed by M. Bestvina and J. Mogilski [5]. A detailed exposition of the theory of absorbing stes (including some applications) can be found in [1]. See also [6] for backgrounds of a related theory of absorbing systems.

1. T. Banakh, T. Radul, M. Zarichnyi Absorbing sets in infinite-dimensional manifolds –1996 ,addr Lviv, VNTL Publishers

2. T. O. Tkach On topology of completed space of monotone functions // preprint

3. T. Dobrowolski, L. Rubin The space of ANR's in $\Bbb R^n$ // Fund. Math. V.146 --1994 p.31--58

4. R. Pol On Borel-measurable collections of counable unions of finite-dimensioanal compacta // Bull. Pol. Acad. Sci. V.32–1984 p.703–713

5. M. Bestvina, J. Mogilski Characterizing certain incomplete infinite-dimensional absolute retracts// Michigan Math. J. V.33– 1986 p.291–313

6. J. Baars, H. Gladdines, J. van Mill Absorbing systems in infinite dimensional manifolds// Top. Appl. V.50–1993 p.147–182

7. D. W. Curtis, R.M. Schori Hyperspaces of Peano continua are Hilbert cubes// Fund. Math. V.101–1978 p.19–38

8. L. Montejano The hyperspace of compact convex subsets of an open subset of $\Bbb R^n$// Bull. Pol. Acad. Sci. Math. V.35--1987 p.793--799

	Problems on absorbing sets in the hyperspace theory and the theory of functions
Author	Bazylevych L., Tkach O., Zarichnyi M. State University “Lviv Polytechnica”,Lviv Regional Institute of Education,Lviv University, Department of Mechanics and Mathematics
Abstract	The method of absorbing sets, which has its origin in the works of Anderson, Bessaga and Pełczyński, is now one of the most powerful tools of infinite-dimensioanl topology having numerous applications not only in topology but also in other areas of mathematics. In its modern form, the method of absorbing sets is developed by M. Bestvina and J. Mogilski [5]. A detailed exposition of the theory of absorbing stes (including some applications) can be found in [1]. See also [6] for backgrounds of a related theory of absorbing systems.
Keywords	absorbing sets, infinite-dimensional topology, Anderson-Bessaga-Pełczyński method, absorbing systems
DOI	doi:10.30970/ms.7.2.214-216
Reference	1. T. Banakh, T. Radul, M. Zarichnyi Absorbing sets in infinite-dimensional manifolds –1996 ,addr Lviv, VNTL Publishers 2. T. O. Tkach On topology of completed space of monotone functions // preprint 3. T. Dobrowolski, L. Rubin The space of ANR's in $\Bbb R^n$ // Fund. Math. V.146 --1994 p.31--58 4. R. Pol On Borel-measurable collections of counable unions of finite-dimensioanal compacta // Bull. Pol. Acad. Sci. V.32–1984 p.703–713 5. M. Bestvina, J. Mogilski Characterizing certain incomplete infinite-dimensional absolute retracts// Michigan Math. J. V.33– 1986 p.291–313 6. J. Baars, H. Gladdines, J. van Mill Absorbing systems in infinite dimensional manifolds// Top. Appl. V.50–1993 p.147–182 7. D. W. Curtis, R.M. Schori Hyperspaces of Peano continua are Hilbert cubes// Fund. Math. V.101–1978 p.19–38 8. L. Montejano The hyperspace of compact convex subsets of an open subset of $\Bbb R^n$// Bull. Pol. Acad. Sci. Math. V.35--1987 p.793--799
Pages	214-216
Volume	7
Issue	2
Year	1997
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Problems on absorbing sets in the hyperspace theory and the theory of functions