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Hyperspaces of cones and fans. (English) Zbl 0413.57010


MSC:

57N20 Topology of infinite-dimensional manifolds
54F15 Continua and generalizations
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References:

[1] R. D. Anderson, Topological properties of the Hilbert cube and the infinite product of open intervals, Trans. Amer. Math. Soc. 126 (1967), 200 – 216. · Zbl 0152.12601
[2] T. A. Chapman, Lectures on Hilbert cube manifolds, American Mathematical Society, Providence, R. I., 1976. Expository lectures from the CBMS Regional Conference held at Guilford College, October 11-15, 1975; Regional Conference Series in Mathematics, No. 28. · Zbl 0317.57009
[3] J. J. Charatonik, On fans, Dissertationes Math. Rozprawy Mat. 54 (1967), 39. · Zbl 0163.44604
[4] D. W. Curtis, Hyperspaces of noncompact metric spaces, Compositio Math. 40 (1980), no. 2, 139 – 152. · Zbl 0431.54004
[5] D. W. Curtis and R. M. Schori, Hyperspaces of Peano continua are Hilbert cubes, Fund. Math. 101 (1978), no. 1, 19 – 38. · Zbl 0409.54044
[6] R. Duda, On the hyperspace of subcontinua of a finite graph. I, Fund. Math. 62 (1968), 265 – 286. R. Duda, On the hyperspace of subcontinua of a finite graph. II, Fund. Math. 63 (1968), 225 – 255. · Zbl 0167.51401
[7] R. Duda, On the hyperspace of subcontinua of a finite graph. I, Fund. Math. 62 (1968), 265 – 286. R. Duda, On the hyperspace of subcontinua of a finite graph. II, Fund. Math. 63 (1968), 225 – 255. · Zbl 0167.51401
[8] James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. · Zbl 0144.21501
[9] Carl Eberhart, Intervals of continua which are Hilbert cubes, Proc. Amer. Math. Soc. 68 (1978), no. 2, 220 – 224. · Zbl 0398.54019
[10] Carl Eberhart, A note on smooth fans, Colloq. Math. 20 (1969), 89 – 90. · Zbl 0184.48102
[11] J. B. Fugate, Retracting fans onto finite fans, Fund. Math. 71 (1971), no. 2, 113 – 125. · Zbl 0214.49701
[12] Michael Handel, On certain sums of Hilbert cubes, General Topology and Appl. 9 (1978), no. 1, 19 – 28. · Zbl 0496.57008
[13] K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. · Zbl 0158.40901
[14] S. B. Nadler, Jr., Hyperspaces of sets–A text with research questions, Pure and Applied Math. Series, vol. 49, Marcel Dekker, New York, 1978. · Zbl 0432.54007
[15] R. B. Sher, The union of two Hilbert cubes meeting in a Hilbert cube need not be a Hilbert cube, Proc. Amer. Math. Soc. 63 (1977), no. 1, 150 – 152. · Zbl 0355.57005
[16] H. Toruńczyk, On CE-images of the Hilbert cube and characterizations of Q-manifolds (preprint).
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