Digitally continuous multivalued functions

Authors:
Carmen Escribano;Antonio Giraldo;María Asunción Sastre
Affiliations:
Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica, Madrid, Spain;Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica, Madrid, Spain;Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica, Madrid, Spain
Venue:
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Year:
2008

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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.