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- W4242152696 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 Jonesâ 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 $X$." @default.
- W4242152696 created "2022-05-12" @default.
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- W4242152696 date "1988-11-01" @default.
- W4242152696 modified "2023-09-27" @default.
- W4242152696 title "Decompositions of Continua Over the Hyperbolic Plane" @default.
- W4242152696 doi "https://doi.org/10.2307/2001121" @default.
- W4242152696 hasPublicationYear "1988" @default.
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