## Decompositions of continua over the hyperbolic plane

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- by James T. Rogers
- Trans. Amer. Math. Soc.
**310**(1988), 277-291 - DOI: https://doi.org/10.1090/S0002-9947-1988-0965753-1
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## Abstract:

The following theorem is proved. Theorem.*Let*$X$

*be a homogeneous continuum such that*${H^1}(X) \ne 0$. If $\mathcal {G}$

*is the collection of maximal terminal proper subcontinua of*$X$,

*then*(1)

*The collection*$\mathcal {G}$

*is a monotone, continuous, terminal decomposition of*$X$, (2)

*The nondegenerate elements of*$\mathcal {G}$

*are mutually homeomorphic, indecomposable, cell-like, terminal, homogeneous continua of the same dimension as*$X$, (3)

*The quotient space is a homogeneous continuum, and*(4)

*The quotient space does not contain any proper, nondegenerate, terminal subcontinuum*. This theorem is related to the Jones’ Aposyndetic Decomposition Theorem. The proof involves the hyperbolic plane and a subset of the circle at $\infty$, called the set of ends of a component of the universal cover of $X$.

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## Bibliographic Information

- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**310**(1988), 277-291 - MSC: Primary 54F20; Secondary 54B15, 54F50
- DOI: https://doi.org/10.1090/S0002-9947-1988-0965753-1
- MathSciNet review: 965753