Zero-dimensional closed set aposyndesis and symmetric Products

• Autores: Alejandro Illanes, Jorge M. Martínez-Montejano
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 37, Nº 4, 2011, págs. 1333-1346
• Idioma: inglés
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• Resumen

  • A continuum is a compact, connected, metric space. It is said that a continuum X is zero-dimensional closed set aposyndetic provided that for each zero-dimensional closed subset A of X and for each p in X minus A, there exists a subcontinuum M of X such that p is in the interior of M and M does not intersect A. In this paper we show that if X is a continuum and n is greater or equal to two, then the n-fold symmetric product of X is zero-dimensional closed set aposyndetic.