Fans are not c-determined

• Autorzy: Alejandro Illanes
• Języki publikacji: EN

Abstrakty

EN

A continuum is a compact connected metric space. For a continuum X, let C(X) denote the hyperspace of subcontinua of X. In this paper we construct two nonhomeomorphic fans (dendroids with only one ramification point) X and Y such that C(X) and C(Y) are homeomorphic. This answers a question by Sam B. Nadler, Jr.

Słowa kluczowe

EN

C-determined; hyperspaces; fan; continuum

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 81
• Numer: 2
• Strony: 299-308

Daty

wydano

1999

otrzymano

1998-11-16

poprawiono

1999-03-25

Twórcy

autor

Alejandro Illanes

• Instituto de Matemáticas, Circuito Exterior, Cd. Universitaria México, 04510, México

Bibliografia

• [1] G. Acosta, Hyperspaces with unique hyperspace, preprint.
• [2] R. D. Anderson, Topological properties of the Hilbert cube and the infinite product of open intervals, Trans. Amer. Math. Soc. 126 (1967), 200-216.
• [3] R. Duda, On the hyperspace of subcontinua of a finite graph, I, Fund. Math. 69 (1968), 265-286.
• [4] C. Eberhart and S. B. Nadler, Jr., Hyperspaces of cones and fans, Proc. Amer. Math. Soc. 77 (1979), 279-288.
• [5] A. Illanes, Chainable continua are not C-determined, Topology Appl., to appear.
• [6] J. Krasinkiewicz, On the hyperspaces of snake-like and circle-like continua, Fund. Math. 83 (1974), 155-164.
• [7] S. Macías, On C-determined continua, Glas. Mat., to appear.
• [8] S. Macías, Hereditarily indecomposable continua have unique hyperspace $2^X$, preprint.
• [9] S. B. Nadler, Jr., Hyperspaces of Sets, Monographs Textbooks Pure Appl. Math. 49, Marcel Dekker, New York, 1978.
• [10] L. E. Ward, Extending Whitney maps, Pacific J. Math. 93 (1981), 465-469.