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Suppose that K is a CW-complex, X is an inverse sequence of stratifiable spaces, and X = lim X. Using the concept of semi-sequence, we provide a necessary and sufficient condition for X to be an absolute co-extensor for K in terms of the inverse sequence X and without recourse to any specific properties of its limit. To say that X is an absolute co-extensor for K is the same as saying that K is an absolute extensor for X, i.e., that each map ƒ : A → K from a closed subset A of X extends to a map F : X → K. Incase K is & polyhedron |/C|cw (the set \K\ with the weak topology CW), we determine a similar characterization that takes into account the simplicial structure of K.
Słowa kluczowe
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Tom
Strony
243--259
Opis fizyczny
Bibliogr. 17 poz.
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autor
autor
- Department of Mathematics, University of Zagreb, Unska 3 P.O. Box 148, 10001 Zagreb, Croatia, ivan.ivansic@fer.hr
Bibliografia
- [1] C. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1-16.
- [2] R. Cauty, Convexite topologique et prolongement des fonctions continues, Compos.Math. 27 (1973), 233-273.
- [3] J. Ceder, Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105-125.
- [4] A. Chigogidze and V. Valov, Universal metric spaces and extension dimension, Topology Appl. 113 (2001), 23-27.
- [5] A. Dranishnikov and J. Dydak, Extension dimension and extension types, Trudy Mat. Inst. Steklova 212 (1996), 61-94 (in Russian).
- [6] I. Ivansic and L. Rubin, The extension dimension of universal spaces, Glas. Mat. Ser. Ill 38(58) (2003), 121-127.
- [7] —, —, Limit theorem for semi-sequences in extension theory, Houston J. Math. 31 (2005), 787-807.
- [8] —, —, Some applications of semi-sequences to extension theory, Topology Proc., to appear.
- [9] M. Levin, On extensional dimension of metrizable spaces, preprint.
- [10] S. Mardešić, Extension dimension of inverse limits, Glas. Mat. Ser. Ill 35(55) (2000), 339-354.
- [11] S. Mardešić and J. Segal, Shape Theory, North-Holland, Amsterdam, 1982.
- [12] R. Millspaugh, L. Rubin and P. Schapiro, Irreducible representations of metrizable spaces, and strongly countable-dimensional spaces, Fund. Math. 148 (1995), 223-256.
- [13] K. Nagami, Finite-to-one closed mappings and dimension. II, Proc. Japan Acad. 35 (1959), 437-439.
- [14] —, Mappings of finite order, Japan J. Math. 30 (1960), 25-54.
- [15] L. Rubin, Cohomological dimension and approximate limits, Proc. Amer. Math. Soc. 125 (1997), 3125-3128.
- [16] —, A stronger limit theorem in extension theory, Glas. Mat. Ser. Ill 36(56) (2001), 95-103.
- [17] L. Rubin and P. Schapiro, Limit theorem for inverse sequences of metric spaces in extension theory, Pacific J. Math. 187 (1999), 177-186
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Bibliografia
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bwmeta1.element.baztech-article-BAT5-0017-0093