continuum. By the hypezspace of X we mean C(X) = {A : A is a: nonempty subcontinuum of X) with the HausdorfI metric. The suspension S(X) of X is the quotient space (X .x I-1, + l])/R, where X X'[ -1, + 1] is the Cartesian product of X and the closed interval [ -1, + l] and R is the equivalence relat
Continua Whose Cone and Hyperspace are Homeomorphic
โ Scribed by Sam B. Nadler, Jr.
- Book ID
- 125682750
- Publisher
- American Mathematical Society
- Year
- 1977
- Tongue
- English
- Weight
- 640 KB
- Volume
- 230
- Category
- Article
- ISSN
- 0002-9947
- DOI
- 10.2307/1997722
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We investigate continua with the property that the cone ojGrer\* the continuum is homeomorphic to the hyperspace of subcontinua of the cantMum. Among our results ale the following theorems: (i) Such a finite-dimensional continuum must be airiodic and onedimensional; (ii) if such a continuum is hered
Let Y be a compact metric space that is not an (n -1)-sphere. If the cone over Examples are given to show that the converse of the first part is false (for n 5) and that the second part does not extend beyond n = 4. An application concerning when hyperspaces of simple n-ods are cones over unique co