The direct limit of metrizable ANR's is an ANR for stratifiable spaces

T.O.Banakh

It is proven that the direct limit $\varinjlim X_n$ of a sequence $X_1\subset X_2\subset\dots$ metrizable A(N)R's is an A(N)R for stratifiable spaces.

1. Banakh T. On topological groups containing a Fréchet-Urysohn fan, Matem. Studii, 9 (1998) no.2, 149–154.

2. Banakh T. Topological classification of strong nuclear (LF)-spaces, Studia Math., 138 (2000), 201–208.

3. Banakh T., Zdomsky L. The topological structure of (homogeneous) spaces and groups with countable cs*-character, Appl. Gen. Top. (to appear)

4. Базилевич Л., Зарічний М. Вступ до теорії нескінченновимірних многовидів, ІЗМН. Київ, 1996, 40 с.

5. Bessaga C., Pe czyński A. Selected topics in infinite-dimensional topology, PWN, Warsaw, 1975.

6. Borges C.J.R. On stratifiable spaces, Pacific J. Math., 17 (1966), 1–16.

7. Cauty R. Convexité topologique et prolongement des fonctions continues, Compositio Math., 27 (1973), 233–271.

8. Cauty R. Sur les rétractes absolus Pₙ-valués de dimension finie, preprint.

9. Ceder J.G. Some generalizations of metric spaces, Pacific J. Math., 11 (1961), 105–126.

10. Dobrowolski T., Toruńczyk H. Separable complete ANR's admitting a group structure are Hilbert manifolds, Top. Appl. 12 (1981), 229–235.

11. Dugundji J. An extension of Tietze's theorem, Pacific J. Math., 1 (1951), 353–367.

12. Engelking R. General topology, PWN, Warsaw, 1977.

13. Gruenhage G. Generalized metric spaces, Handbook of Set-Theoretic Topology (K.Kunen and J.Vaughan, eds.) Elsevier, Amsterdam, 1984, 423–501 p.

14. Hausdorff F. Erweiterung einer stetigen Abbildung, Fund. Math., 30 (1938), 40–47.

15. Hu S.-T. Theory of Retracts, Detroit, Wayne State Univ. Press, 1965.

16. Kodama Y. Note on an absolute neighborhood extensor for metric spaces, J. Math. Soc. of Japan, 8, no.3, 206–215.

17. Pentsak E. On manifolds modeled on direct limits of 𝒞-universal ANR's, Matematychni Studii (1995), no.5, 107–116.

18. Sakai K. On ℝ^∞-manifolds and Q^∞-manifolds, Topology Appl., 18 (1984), 69–79.

	The direct limit of metrizable ANR's is an ANR for stratifiable spaces
Author	T.O.Banakh Ivan Franko National University of Lviv
Abstract	It is proven that the direct limit $\varinjlim X_n$ of a sequence $X_1\subset X_2\subset\dots$ metrizable A(N)R's is an A(N)R for stratifiable spaces.
Keywords	direct limit, stratifiable space, metrizable ANR
DOI	doi:10.30970/ms.23.1.92-98
Reference	1. Banakh T. On topological groups containing a Fréchet-Urysohn fan, Matem. Studii, 9 (1998) no.2, 149–154. 2. Banakh T. Topological classification of strong nuclear (LF)-spaces, Studia Math., 138 (2000), 201–208. 3. Banakh T., Zdomsky L. The topological structure of (homogeneous) spaces and groups with countable cs*-character, Appl. Gen. Top. (to appear) 4. Базилевич Л., Зарічний М. Вступ до теорії нескінченновимірних многовидів, ІЗМН. Київ, 1996, 40 с. 5. Bessaga C., Pe czyński A. Selected topics in infinite-dimensional topology, PWN, Warsaw, 1975. 6. Borges C.J.R. On stratifiable spaces, Pacific J. Math., 17 (1966), 1–16. 7. Cauty R. Convexité topologique et prolongement des fonctions continues, Compositio Math., 27 (1973), 233–271. 8. Cauty R. Sur les rétractes absolus Pₙ-valués de dimension finie, preprint. 9. Ceder J.G. Some generalizations of metric spaces, Pacific J. Math., 11 (1961), 105–126. 10. Dobrowolski T., Toruńczyk H. Separable complete ANR's admitting a group structure are Hilbert manifolds, Top. Appl. 12 (1981), 229–235. 11. Dugundji J. An extension of Tietze's theorem, Pacific J. Math., 1 (1951), 353–367. 12. Engelking R. General topology, PWN, Warsaw, 1977. 13. Gruenhage G. Generalized metric spaces, Handbook of Set-Theoretic Topology (K.Kunen and J.Vaughan, eds.) Elsevier, Amsterdam, 1984, 423–501 p. 14. Hausdorff F. Erweiterung einer stetigen Abbildung, Fund. Math., 30 (1938), 40–47. 15. Hu S.-T. Theory of Retracts, Detroit, Wayne State Univ. Press, 1965. 16. Kodama Y. Note on an absolute neighborhood extensor for metric spaces, J. Math. Soc. of Japan, 8, no.3, 206–215. 17. Pentsak E. On manifolds modeled on direct limits of 𝒞-universal ANR's, Matematychni Studii (1995), no.5, 107–116. 18. Sakai K. On ℝ^∞-manifolds and Q^∞-manifolds, Topology Appl., 18 (1984), 69–79.
Pages	92-98
Volume	23
Issue	1
Year	2005
Journal	Matematychni Studii
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