Generating and inserting continuous functions with values in bounded complete domains and hedgehog-like structures

• Autores: Francisco Javier Gutierrez García , Tomasz Kubiak , María Angeles de Prada Vicente
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 1, 2008, págs. 123-144
• Idioma: inglés
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• Resumen

  • The paper deals with functions on a topological space having values in a bounded complete domain. Our purpose is two-fold. We first develop a theory of generating such functions from certain scales or prescales of subsets. We then study lower and upper limits of functions having bounded complete domain as a range space. We characterize those limit functions in terms of the (pre)scales generating the original ones. Part of these developments is then used to prove an insertion-type theorem for continuous functions from a topological space to an appropriately based bounded complete domain with its Lawson topology. Examples of those domains include, among others, hedgehogs with countably many spines, their products as well as various ¿mutants¿ of the hedgehog