The strongly universal property in 
convex sets

T. Banakh

It is shown that a separable linear metric AR-space $L$ is strongly $C$-universal, where $C$ is a class of spaces, if and only if $L$ contains a convex closed strongly $C$-universal subspace. We inspect also the strongly $C$-universal property in convex sets containing a $C$-universal closed subset of infinite codimension.

1. T. Banakh Characterization of spaces admitting an embedding with homotopy negligible complement into a~Hilbert manifoldinfo preprint

2. T. Banakh Characterization of convex $Z$-set in linear metric spaces// Functional Anal. Appl.-- 1994 V. 28p. 285--286

3. T.Banakh The~strongly universal property of spaces admitting an algebraic structure info, preprint

4. T. Banakh, R. Cauty Interplay between strongly universal spaces and pairsinfo preprint

5. T. Banakh, T. Dobrowolski, A. Plichko Topology of operator imagesinfo preprint

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

7. M.Bestvina, P.Bowers, J.Mogilski, J.Walsh Characterizing of Hilbert space manifolds revised// Top. Appl.V. 24– 1986p. 53–69

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

9. P.L. Bowers Discrete cells property in the boundary set setting// Proc, Amer. Math. Soc. V. 93– 1985p. 735–740

10. R. Cauty The strongly universal property and its applicationsin Russian// Trudy Mat. Inst. SteklovV. 212–1996 p.95-122

11. D.W. Curtis, T. Dobrowolski, J. Mogilski Some applications of the~topological characterizations of the~sigma-compact spaces $l^2_f$ and $\Sigma$// Trans. Amer. Math. Soc.V. 284-- 1984p. 837-846

12. T. Dobrowolski The compact $Z$-set property in convex sets// Top. Appl.V. 23-- 1986 p. 163-172

13. T. Dobrowolski, W.Marciszewski Rays and the fixed point property in non-compact spaces// Tsukuba J. Math.V.21–1997p.97–112

14. T. Dobrowolski, H. Toruńczyk Separable complete ANR's admitting a group structure are Hilbert manifolds// Top. Appl. V. 12– 1981p. 229-235

15. R. Engelking General topology, PWN,addr Warsaw– 1977

16. Hu S.-T. Theory of Retracts,addr Detroit, Wayne State Univ. Press –1965

17. S. Mardešić, N. Uglešić On irreductible mappings into polyhedra// Top. Appl.– 1995V.61p.187–203

18. H. Toruńczyk Concerning locally homotopy negligible sets and characterization of $l_2$-manifolds// Fund. Math.V. 101-- 1978p. 93--110

19. Va. F.A. Valentine Convex sets, McGraw-Hill Book Company,addr NY Inc.– 1964

	The strongly universal property in convex sets
Author	T. Banakh Department of Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukarine
Abstract	It is shown that a separable linear metric AR-space $L$ is strongly $C$-universal, where $C$ is a class of spaces, if and only if $L$ contains a convex closed strongly $C$-universal subspace. We inspect also the strongly $C$-universal property in convex sets containing a $C$-universal closed subset of infinite codimension.
Keywords	strongly C-universal, convex closed subspace, C-universal property, infinite codimension
DOI	doi:10.30970/ms.10.2.203-218
Reference	1. T. Banakh Characterization of spaces admitting an embedding with homotopy negligible complement into a~Hilbert manifoldinfo preprint 2. T. Banakh Characterization of convex $Z$-set in linear metric spaces// Functional Anal. Appl.-- 1994 V. 28p. 285--286 3. T.Banakh The~strongly universal property of spaces admitting an algebraic structure info, preprint 4. T. Banakh, R. Cauty Interplay between strongly universal spaces and pairsinfo preprint 5. T. Banakh, T. Dobrowolski, A. Plichko Topology of operator imagesinfo preprint 6. T.Banakh, T.Radul, M.Zarichnyi Absorbing sets in infinite-dimensional manifolds, VNTL Publishers,addr Lviv– 1996 7. M.Bestvina, P.Bowers, J.Mogilski, J.Walsh Characterizing of Hilbert space manifolds revised// Top. Appl.V. 24– 1986p. 53–69 8. M. Bestvina, J. Mogilski Characterizing certain incomplete infinite-dimensional absolute retracts// Michigan Math. J.V. 33– 1986p. 291–313 9. P.L. Bowers Discrete cells property in the boundary set setting// Proc, Amer. Math. Soc. V. 93– 1985p. 735–740 10. R. Cauty The strongly universal property and its applicationsin Russian// Trudy Mat. Inst. SteklovV. 212–1996 p.95-122 11. D.W. Curtis, T. Dobrowolski, J. Mogilski Some applications of the~topological characterizations of the~sigma-compact spaces $l^2_f$ and $\Sigma$// Trans. Amer. Math. Soc.V. 284-- 1984p. 837-846 12. T. Dobrowolski The compact $Z$-set property in convex sets// Top. Appl.V. 23-- 1986 p. 163-172 13. T. Dobrowolski, W.Marciszewski Rays and the fixed point property in non-compact spaces// Tsukuba J. Math.V.21–1997p.97–112 14. T. Dobrowolski, H. Toruńczyk Separable complete ANR's admitting a group structure are Hilbert manifolds// Top. Appl. V. 12– 1981p. 229-235 15. R. Engelking General topology, PWN,addr Warsaw– 1977 16. Hu S.-T. Theory of Retracts,addr Detroit, Wayne State Univ. Press –1965 17. S. Mardešić, N. Uglešić On irreductible mappings into polyhedra// Top. Appl.– 1995V.61p.187–203 18. H. Toruńczyk Concerning locally homotopy negligible sets and characterization of $l_2$-manifolds// Fund. Math.V. 101-- 1978p. 93--110 19. Va. F.A. Valentine Convex sets, McGraw-Hill Book Company,addr NY Inc.– 1964
Pages	203-218
Volume	10
Issue	2
Year	1998
Journal	Matematychni Studii
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Table of content of issue	html

The strongly universal property in convex sets