Hyperspaces of Peano continua of euclidean spaces
Gladdines, Helma ; van Mill, Jan
Fundamenta Mathematicae, Tome 142 (1993), p. 173-188 / Harvested from The Polish Digital Mathematics Library

If X is a space then L(X) denotes the subspace of C(X) consisting of all Peano (sub)continua. We prove that for n ≥ 3 the space L(n) is homeomorphic to B, where B denotes the pseudo-boundary of the Hilbert cube Q.

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:211980
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     title = {Hyperspaces of Peano continua of euclidean spaces},
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     year = {1993},
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Gladdines, Helma; van Mill, Jan. Hyperspaces of Peano continua of euclidean spaces. Fundamenta Mathematicae, Tome 142 (1993) pp. 173-188. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv142i2p173bwm/

[00000] [1] J. Baars, H. Gladdines, and J. van Mill, Absorbing systems in infinite-dimensional manifolds, Topology Appl., to appear. | Zbl 0794.57005

[00001] [2] C. Bessaga and A. Pełczyński, Selected Topics in Infinite-Dimensional Topology, PWN, Warszawa 1975.

[00002] [3] M. Bestvina and J. Mogilski, Characterizing certain incomplete infinite dimensional absolute retracts, Michigan Math. J. 33 (1986), 291-313. | Zbl 0629.54011

[00003] [4] R. Cauty, L'espace des fonctions continues d'un espace métrique dénombrable, Proc. Amer. Math. Soc. 113 (1991), 493-501.

[00004] [5] R. Cauty, L'espace des arcs d'une surface, Trans. Amer. Math. Soc. 332 (1992), 193-209. | Zbl 0762.54012

[00005] [6] D. W. Curtis, Hyperspaces of finite subsets as boundary sets, Topology Appl. 22 (1986), 97-107. | Zbl 0575.54009

[00006] [7] D. W. Curtis and R. M. Schori, Hyperspaces of Peano continua are Hilbert cubes, Fund. Math. 101 (1978), 19-38. | Zbl 0409.54044

[00007] [8] J. J. Dijkstra and J. Mogilski, The topological product structure of systems of Lebesgue spaces, Math. Ann. 290 (1991), 527-543. | Zbl 0734.46013

[00008] [9] J. J. Dijkstra, J. van Mill, and J. Mogilski, The space of infinite-dimensional compacta and other topological copies of (lf2)ω, Pacific J. Math. 152 (1992), 255-273. | Zbl 0786.54012

[00009] [10] T. Dobrowolski, W. Marciszewski, and J. Mogilski, On topological classification of function spaces Cp(X) of low Borel complexity, Trans. Amer. Math. Soc. 328 (1991), 307-324. | Zbl 0768.54016

[00010] [11] C. Kuratowski, Evaluation de la classe borélienne ou projective d'un ensemble de points à l'aide des symboles logiques, Fund. Math. 17 (1931), 249-272. | Zbl 57.0092.05

[00011] [12] S. Mazurkiewicz, Sur l'ensemble des continus péaniens, ibid., 273-274. | Zbl 0003.10601

[00012] [13] S. B. Nadler, Hyperspaces of Sets, Marcel Dekker, New York 1978. | Zbl 0432.54007

[00013] [14] J. van Mill, Infinite-Dimensional Topology: prerequisites and introduction, North- Holland, Amsterdam 1989. | Zbl 0663.57001