Inverse limits with set valued functions

• Autores: Van Nall
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 37, Nº 4, 2011, págs. 1323-1332
• Idioma: inglés
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• Resumen

  • We begin to answer the question of which continua can be homeomorphic to an inverse limit with a single upper semi-continuous bonding map from [0,1] to the set of closed subsets of [0,1]. Several continua including [0,1]×[0,1] and all compact manifolds with dimension greater than one cannot be homeomorphic to such an inverse limit. It is also shown that if the upper semi-continuous bonding maps have only zero dimensional pointvalues, then the dimension of the inverse limit does not exceed the dimension of the factor spaces.