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Digitally Continuous Multivalued Functions

  • Carmen Escribano
  • Antonio Giraldo
  • María Asunción Sastre
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4992)

Abstract

We introduce in this paper a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach uses multivalued maps. We show how the multivalued approach provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we characterize the deletion of simple points, one of the most important processing operations in digital topology, as a particular kind of retraction.

Keywords

Digital space continuous function simple point retraction 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Carmen Escribano
    • 1
  • Antonio Giraldo
    • 1
  • María Asunción Sastre
    • 1
  1. 1.Departamento de Matemática Aplicada, Facultad de InformáticaUniversidad PolitécnicaMadridSpain

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