An introduction to homogeneous continua
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Macías, Sergio
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Universidad Industrial de Santander
Abstract
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Un continuo es un espacio métrico, compacto y conexo. Un continuo X es homogéneo si para cualesquiera dos de sus puntos x1 y x2 de X, existe un homeomorfismo h: X -> X tal que h(x1) = x2. Presentaremos un poco de historia, ejemplos y propiedades de este tipo de continuos. Daremos una demostración del Teorema de descomposición aposindética de Jones.
A continuum is a compact, connected, metric space. A continuum X is homogeneous provided that for each pair of points x1 and x2 of X, there exists a homeomorphism h: X->X such that h(x1) = x2. We present a bit of history, examples and properties of this kind of continua. We give a proof of Jones's Aposyndetic Decomposition Theorem.
A continuum is a compact, connected, metric space. A continuum X is homogeneous provided that for each pair of points x1 and x2 of X, there exists a homeomorphism h: X->X such that h(x1) = x2. We present a bit of history, examples and properties of this kind of continua. We give a proof of Jones's Aposyndetic Decomposition Theorem.
Keywords
Circle of pseudo-arcs, continuum, Hilbert cube, Menger universal curve, homogeneous space, monotone map, Jones's set function T, pseudo-arc, Círculo de pseudoarcos, continuo, cubo de Hilbert, curva universal de Menger, espacio homogéneo, función monótona, función T de Jones, pseudoarco