Hyperspaces and cones

Macías, Sergio

doi:10.1090/S0002-9939-97-04175-0

Hyperspaces and cones
HTML articles powered by AMS MathViewer

by Sergio Macías PDF

Proc. Amer. Math. Soc. 125 (1997), 3069-3073 Request permission

Abstract:

We characterize locally connected continua $X$ for which its hyperspace of subcontinua, $\mathcal {C}(X)$, has finite dimension and is homeomorphic to the cone of a continuum $Z$.

References

R. Duda, On the hyperspace of subcontinua of a finite graph. I, Fund. Math. 62 (1968), 265–286. MR 236881, DOI 10.4064/fm-62-3-265-286
A. M. Dilks and J. T. Rogers Jr., Whitney stability and contractible hyperspaces, Proc. Amer. Math. Soc. 83 (1981), no. 3, 633–640. MR 627710, DOI 10.1090/S0002-9939-1981-0627710-3
John G. Hocking and Gail S. Young, Topology, 2nd ed., Dover Publications, Inc., New York, 1988. MR 1016814
Alejandro Illanes, Hyperspaces homeomorphic to cones, Glas. Mat. Ser. III 30(50) (1995), no. 2, 285–294. MR 1381354
Sam B. Nadler Jr., Continua whose cone and hyperspace are homeomorphic, Trans. Amer. Math. Soc. 230 (1977), 321–345. MR 464191, DOI 10.1090/S0002-9947-1977-0464191-0
Sam B. Nadler Jr., Hyperspaces of sets, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 49, Marcel Dekker, Inc., New York-Basel, 1978. A text with research questions. MR 0500811
Sam B. Nadler Jr., Continuum theory, Monographs and Textbooks in Pure and Applied Mathematics, vol. 158, Marcel Dekker, Inc., New York, 1992. An introduction. MR 1192552
James T. Rogers Jr., The cone = hyperspace property, Canadian J. Math. 24 (1972), 279–285. MR 295302, DOI 10.4153/CJM-1972-022-8
James T. Rogers Jr., Continua with cones homeomorphic to hyperspaces, General Topology and Appl. 3 (1973), 283–289. MR 362257