Geodesic
The Cone = Hyperspace Property
Canadian journal of mathematics, Tome 24 (1972) no. 2, pp. 279-285

Voir la notice de l'article provenant de la source Cambridge University Press

The author has recently shown [11] that the hyperspace of subcontinua of a solenoid is homeomorphic to the cone over that solenoid. This is an interesting result, for it is the first time that the hyperspace of subcontinua of a complicated space has been recognized. This homeomorphism, moreover, is the expected map; it maps the singletons onto the base of the cone and the point corresponding to the whole space onto the vertex of the cone. We say that spaces for which such natural homeomorphisms exist have the cone = hyperspace property. In the first section we prove the following theorem. 
Jr., James T. Rogers. The Cone = Hyperspace Property. Canadian journal of mathematics, Tome 24 (1972) no. 2, pp. 279-285. doi: 10.4153/CJM-1972-022-8
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[1] 1. Bing, R. H., The elusive fixed-point property, Amer. Math. Monthly 76 (1969), 119–132. Google Scholar

[2] 2. Bing, R. H., Snake-like continua, Duke Math. J. 18 (1951), 653–663. Google Scholar

[3] 3. Dugundji, J., Topology (Allyn and Bacon, Boston, 1966). Google Scholar

[4] 4. Tom, Ingram, Decomposable circle-like continua, Fund. Math. 63 (1968), 193–198. Google Scholar

[5] 5. Kelley, J. L., Hyperspaces of a continuum, Trans. Amer. Math. Soc. 52 (1942), pp. 22–36. Google Scholar

[6] 6. Knill, R. J., Cones, products and fixed points, Fund. Math. 60 (1967), 35–46. Google Scholar

[7] 7. Kuratowski, K., Topology, Volume II (Academic Press, New York, 1968). Google Scholar

[8] 8. Sam B., Nadler, Jr., Multicoherence techniques applied to inverse limits, Trans. Amer. Math. Soc. 157 (1971), 227–234. Google Scholar

[9] 9. Rhee, C. J., On dimension of hyperspaces of a metric continuum, Bull. Soc. Roy. Sci. Liège 38 (1969), 602–604. Google Scholar

[10] 10. James T., Rogers, Jr., Dimension of hyperspaces, Bull. Pol. Acad. Sci. 19 (1971) 25–27. Google Scholar

[11] 11. James T., Rogers, Jr., Embedding the hyper space of a circle-like plane continua, Proc. Amer. Math. Soc. 29 (1971), 165–168. Google Scholar

[12] 12. Young, G. S., Fixed-point theorems for arcwise connected continua, Proc. Amer. Math. Soc. 11 (1960), 880–884. Google Scholar

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