It is shown that the hyperspace of a connected CW-complex is an absolute retract for stratifiable spaces, where the hyperspace is the space of non-empty compact (connected) sets with the Vietoris topology.
Institute of Mathematics, University of Tsukuba, Tsukuba-city 305, Japan
Bibliografia
[Bo1] C. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1-16.
[Bo2] C. R. Borges, A study of absolute extensor spaces, ibid. 31 (1969), 609-617.
[Bo3] C. R. Borges, Absolute extensor spaces: A correction and an answer, ibid. 50 (1974), 29-30.
[Bo4] C. R. Borges, Connectivity of function spaces, Canad. J. Math. 5 (1971), 759-763.
[Ca1] R. Cauty, Sur les sous-espaces des complexes simpliciaux, Bull. Soc. Math. France 100 (1972), 129-155.
[Ca2] R. Cauty, Sur le prolongement des fonctions continues à valeurs dans CW-complexes, C. R. Acad. Sci. Paris Sér. A 274 (1972), 35-37.
[Ca3] R. Cauty, Convexité topologique et prolongement des fonctions continues, Compositio Math. 27 (1973), 133-271.
[Ca4] R. Cauty, Rétraction dans les espaces stratifiables, Bull. Soc. Math. France 102 (1974), 129-149.
[Ca5] R. Cauty, Sur les espaces d'applications dans les CW-complexes, Arch. Math. (Basel) 27 (1976), 306-311.
[Ce] J. G. Ceder, Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105-126.
[CP] D. W. Curtis and D. S. Patching, Hyperspaces of direct limits of locally compact metric spaces, Topology Appl. 29 (1988), 55-60.
[CP] D. W. Curtis and R. M. Schori, Hyperspaces of polyhedra are Hilbert cubes, Fund. Math. 99 (1978), 189-197.
[CS1] D. W. Curtis and R. M. Schori, Hyperspaces of Peano continua are Hilbert cubes, ibid. 101 (1978), 19-38.
[Gr] G. Gruenhage, Stratifiable spaces are $M_2$, Topology Proc. 1 (1976), 221-226.
[Ju] H. J. K. Junnila, Neighbornets, Pacific J. Math. 76 (1978), 83-108.
[Ke] J. L. Kelley, Hyperspaces of a continuum, Trans. Amer. Math. Soc. 52 (1942), 22-36.
[Mi] T. Mizokami, On CF families and hyperspaces of compact subsets, Topology Appl. 35 (1990), 75-92.
[MK] T. Mizokami and K. Koiwa, On hyperspaces of compact and finite subsets, Bull. Joetsu Univ. of Education 6 (1987), 1-14.
[Ta] U. Tašmetov, On the connectedness of hyperspaces, Dokl. Akad. Nauk SSSR 215 (1974), 286-288 (in Russian); English transl.: Soviet Math. Dokl. 15 (1974), 502-504.
[Wo] M. Wojdysławski, Rétractes absolus et hyperespaces des continus, Fund. Math. 32 (1939), 184-192.
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