On 
manifolds modeled on direct limits of $\mathcal C$-universal ANR's

Eugen Pentsak

Countable direct limits of strongly $\mathcal C$-universal ANR-spaces are considered. Characterization theorems for these spaces and corresponding manifold are proved. Besides, open (closed) embedding theorem and classification theorems are proved for manifolds.

1. Heisey R.E. Manifolds modelled on $\Bbb R^\infty$ or bounded weak${}^*$- topologies// Trans. Amer. Math. Soc., 1975. v.206. p.295-312.

2. Heisey R.E. Manifolds modelled on the direct limit of Hilbert cubes// Geometric Topology, New York, Academic Press, 1979. p.609-619.

3. Heisey R.E., Toruńczyk H. On the topology of direct limits of $ANR$s// Pacif. J. Math., 1981. v.93. N2. p.307-312.

4. Sakai K. On $\Bbb R^\infty$-manifolds and $ Q^\infty$-manifolds.// Topology Appl., 1984. v.18. p.69-79.

5. Sakai K. On $\Bbb R^\infty$-manifolds and $ Q^\infty$-manifolds, II: Infinite deficiency.//Tsukuba J.Math., 1984. v.8. N1, p.101-118.

6. Liem V.T. An $\alpha$-approximation theorem for $ Q^\infty$-manifolds.// Proc. Amer. Math. Soc., 1981. v.82. p.125-132.

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

8. Curtis D.W., Patching D.S. Hyperspaces of direct limit of locally compact metric spaces.// Topology and its Applications, 1988. v.29.

9. Cauty R. Ensembles absorbants pour les classes projectives.// Fund. Math., 1993. v.143. p.203-206.

10. Morita K. On spaces having the weak topology with respect to closed covering. // Proc. Japan Acad., 1954. v.30. p.711-717.

11. Mill J. van. Infinite-dimensional topology.Prerequisites and Introduction.– North-Holand, 1989.

12. Kodama Y. Note on an absolute neighbourhood extensor for metric spaces.// Journal of the Math. Soc. of Japan,1956.v.8.N3,p.206-215.

13. Банах Т.О. О непрерывных алгебраических операциях на прямых пределах метрических пространств. Препринт, 1995.

14. Eнгелькинг P. Общая топология.-- М.: Мир, 1986.

15. Hu S.-T. Theory of retracts.– Detroit, Wayne State University Press, 1965.

16. Bessaga C., Pelczyński A. Selected topics in infinite-dimensional topology.// Warszawa, 1975.

17. Hansen V.L. Some theorems on direct limits of expanding sequences of manifolds.// Math. Scand., 1971. v.29. p.5-36. Department of Mathematic, Lviv University Universitetska 1, 290602, Ukraine

	On manifolds modeled on direct limits of $\mathcal C$-universal ANR's
Author	Eugen Pentsak Ivan Franko National University of Lviv, Department of Mechanics and Mathematics, Universytetska 1, Lviv, 79000, Ukraine
Abstract	Countable direct limits of strongly $\mathcal C$-universal ANR-spaces are considered. Characterization theorems for these spaces and corresponding manifold are proved. Besides, open (closed) embedding theorem and classification theorems are proved for manifolds.
Keywords	ANR-spaces, C-universal ANR-spaces, manifolds, homeomorphism, triangulation, direct limits, homotopy, embeddings, theorem and classification theorems
DOI	doi:10.30970/ms.5.1.107-116
Reference	1. Heisey R.E. Manifolds modelled on $\Bbb R^\infty$ or bounded weak${}^*$- topologies// Trans. Amer. Math. Soc., 1975. v.206. p.295-312. 2. Heisey R.E. Manifolds modelled on the direct limit of Hilbert cubes// Geometric Topology, New York, Academic Press, 1979. p.609-619. 3. Heisey R.E., Toruńczyk H. On the topology of direct limits of $ANR$s// Pacif. J. Math., 1981. v.93. N2. p.307-312. 4. Sakai K. On $\Bbb R^\infty$-manifolds and $ Q^\infty$-manifolds.// Topology Appl., 1984. v.18. p.69-79. 5. Sakai K. On $\Bbb R^\infty$-manifolds and $ Q^\infty$-manifolds, II: Infinite deficiency.//Tsukuba J.Math., 1984. v.8. N1, p.101-118. 6. Liem V.T. An $\alpha$-approximation theorem for $ Q^\infty$-manifolds.// Proc. Amer. Math. Soc., 1981. v.82. p.125-132. 7. Bestvina M., Mogilski J. Characterizing certain incomplete infinite-dimensional absolute retracts.// Michigan Math. J., 1986. v.33. p. 291-313. 8. Curtis D.W., Patching D.S. Hyperspaces of direct limit of locally compact metric spaces.// Topology and its Applications, 1988. v.29. 9. Cauty R. Ensembles absorbants pour les classes projectives.// Fund. Math., 1993. v.143. p.203-206. 10. Morita K. On spaces having the weak topology with respect to closed covering. // Proc. Japan Acad., 1954. v.30. p.711-717. 11. Mill J. van. Infinite-dimensional topology.Prerequisites and Introduction.– North-Holand, 1989. 12. Kodama Y. Note on an absolute neighbourhood extensor for metric spaces.// Journal of the Math. Soc. of Japan,1956.v.8.N3,p.206-215. 13. Банах Т.О. О непрерывных алгебраических операциях на прямых пределах метрических пространств. Препринт, 1995. 14. Eнгелькинг P. Общая топология.-- М.: Мир, 1986. 15. Hu S.-T. Theory of retracts.– Detroit, Wayne State University Press, 1965. 16. Bessaga C., Pelczyński A. Selected topics in infinite-dimensional topology.// Warszawa, 1975. 17. Hansen V.L. Some theorems on direct limits of expanding sequences of manifolds.// Math. Scand., 1971. v.29. p.5-36. Department of Mathematic, Lviv University Universitetska 1, 290602, Ukraine
Pages	107-116
Volume	5
Issue	1
Year	1995
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

On manifolds modeled on direct limits of $\mathcal C$-universal ANR's