Decompositions of Continua over the Hyperbolic Plane
نویسنده
چکیده
The following theorem is proved. THEOREM. Let X be a homogeneous continuum such that Hl(X) ^ 0. Ij'$/ is the collection of maximal terminal proper subcontinua of X, then (1) The collection ff is a monotone, continuous, terminal decomposition ofX, (2) The nondegenerate elements of%? 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
منابع مشابه
History of Continuum Theory
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 2 Basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 3 The Jordan Curve Theorem and the concept of a curve . . . . . . . . . . . . . . . . . 707 4 Local connectedness; plane continua.. . . . . ....
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