Universal Nöbeling spaces and
pseudo-boundaries 
of Euclidean spaces

A. Chigogidze; M. M. Zarichnyi

1. S. M. Ageev, Axiomatic method of partitions in the theory of Menger and Nöbeling spaces, preprint (in Russian).

2. T. Banakh, Characterization of spaces admitting a homotopy dense embedding into a Hilbert manifold, Topology Appl. 86 (1998), 123–131.

3. T. Banakh, T. Radul and M. Zarichnyi, Absorbing Sets in Infinite-Dimensional manifolds, VNTL Publishers, Lviv, 1996.

4. M. Bestvina, Characterizing $k$-dimensional universal Menger compacta, Memoirs Amer. Math. Soc. No. 370, 71, 1988.

5. M. Bestvina, J. Mogilski, Characterizing certain incomplete infinite-dimensional absolute retracts, Michigan Math. J. 33 (1986), 291–13.

6. A. Chigogidze, Inverse Spectra, North Holland, Amsterdam, 1996.

7. A. Chigogidze, K. Kawamura and E. D. Tymchatyn, Nöbeling spaces and pseudo-interiors of Menger compacta, Topology Appl. 68 (1996), 33-65.

8. A. Chigogidze, The theory of n-shapes, Russian Math. Surveys, 44:5 (1989), 145-174.

9. J. J. Dikstra, J. van Mill and J. Mogilski, Classification of finite-dimensional universal pseudo-boundaries and pseudo-interiors, Trans. Amer. Math. Soc. 332 (1992), 693–709.

10. T. Dobrowolski, W. Marciszewski, Rays and the fixed point property in inoncompact spaces, Tsukuba Math. J. 21 (1997), 97–112.

11. T. Dobrowolski, J. Mogilski, Problems on topological classification of incomplete metric spaces, Open Problems in Topology (J. van Mill and G. M. Reed, eds.), North Holland, New York, 1990, 409–429.

12. R. Geoghegan, R. R. Summerhill, Pseudo-boundaries and pseudo-interiors in euclidean spaces and topological manifolds, Trans. Amer. Math. Soc. 194 (1974), 141–165.

13. H. Gladdines, Absorbing systems in infinite-dimensional manifolds and applications, Ph.D. thesis, Vrije Universiteit, Amsterdam, the Netherlands, 1994.

14. J. Mogilski, Characterizing the topology of infinite dimensional $\sigma$-compact manifolds, Proc. Amer. Math. Soc. 92 (1984), 111--118.

15. H. Toruńczyk, Concerning locally homotopy negligible sets and characterization of $\ell_{2}$-manifolds, Fund. Math. 101 (1978), 93--110.

16. J. E. West, Open problems in infinite-dimensional topology, Open Problems in Topology (J. van Mill and G. M. Reed, eds.), North Holland, New York, 1990, 523–597.

17. M. M. Zarichnyi, Absorbing sets for $n$-dimensional spaces n absolute Borel and projective classes, Mathematics Sbornik 188 (1997), 113--126.

	Universal Nöbeling spaces and pseudo-boundaries of Euclidean spaces
Author	A. Chigogidze, M. M. Zarichnyi chigogid@math.usask.ca, mzar@litech.lviv.ua Department ,of Mathematics and Statistics, University of Saskatchewan, ,McLean Hall, ,106 ,Wiggins Road, Saskatoon, SK, S7N ,5E6, Canada , , Faculty of Mechanics and ,Mathematics, Lviv Ivan Franko National University, ,Universytets'ka 1, 79000 ,Lviv, ,Ukraine
Abstract	We give a topological characterization of the $n$-dimensional pseudoboundary of the $(2n + 1)$-dimensional Euclidean space.
Keywords	topological characterization, $n$-dimensional pseudoboundary, $(2n + 1)$-dimensional Euclidean space
DOI	doi:10.30970/ms.19.2.193-200
Reference	1. S. M. Ageev, Axiomatic method of partitions in the theory of Menger and Nöbeling spaces, preprint (in Russian). 2. T. Banakh, Characterization of spaces admitting a homotopy dense embedding into a Hilbert manifold, Topology Appl. 86 (1998), 123–131. 3. T. Banakh, T. Radul and M. Zarichnyi, Absorbing Sets in Infinite-Dimensional manifolds, VNTL Publishers, Lviv, 1996. 4. M. Bestvina, Characterizing $k$-dimensional universal Menger compacta, Memoirs Amer. Math. Soc. No. 370, 71, 1988. 5. M. Bestvina, J. Mogilski, Characterizing certain incomplete infinite-dimensional absolute retracts, Michigan Math. J. 33 (1986), 291–13. 6. A. Chigogidze, Inverse Spectra, North Holland, Amsterdam, 1996. 7. A. Chigogidze, K. Kawamura and E. D. Tymchatyn, Nöbeling spaces and pseudo-interiors of Menger compacta, Topology Appl. 68 (1996), 33-65. 8. A. Chigogidze, The theory of n-shapes, Russian Math. Surveys, 44:5 (1989), 145-174. 9. J. J. Dikstra, J. van Mill and J. Mogilski, Classification of finite-dimensional universal pseudo-boundaries and pseudo-interiors, Trans. Amer. Math. Soc. 332 (1992), 693–709. 10. T. Dobrowolski, W. Marciszewski, Rays and the fixed point property in inoncompact spaces, Tsukuba Math. J. 21 (1997), 97–112. 11. T. Dobrowolski, J. Mogilski, Problems on topological classification of incomplete metric spaces, Open Problems in Topology (J. van Mill and G. M. Reed, eds.), North Holland, New York, 1990, 409–429. 12. R. Geoghegan, R. R. Summerhill, Pseudo-boundaries and pseudo-interiors in euclidean spaces and topological manifolds, Trans. Amer. Math. Soc. 194 (1974), 141–165. 13. H. Gladdines, Absorbing systems in infinite-dimensional manifolds and applications, Ph.D. thesis, Vrije Universiteit, Amsterdam, the Netherlands, 1994. 14. J. Mogilski, Characterizing the topology of infinite dimensional $\sigma$-compact manifolds, Proc. Amer. Math. Soc. 92 (1984), 111--118. 15. H. Toruńczyk, Concerning locally homotopy negligible sets and characterization of $\ell_{2}$-manifolds, Fund. Math. 101 (1978), 93--110. 16. J. E. West, Open problems in infinite-dimensional topology, Open Problems in Topology (J. van Mill and G. M. Reed, eds.), North Holland, New York, 1990, 523–597. 17. M. M. Zarichnyi, Absorbing sets for $n$-dimensional spaces n absolute Borel and projective classes, Mathematics Sbornik 188 (1997), 113--126.
Pages	193-200
Volume	19
Issue	2
Year	2003
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Universal Nöbeling spaces and pseudo-boundaries of Euclidean spaces