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A Fixed Point Theorem in a Category of Compact Metric Spaces \Lambda
 

Summary: A Fixed Point Theorem
in a Category of Compact Metric Spaces \Lambda
Fabio Alessi, Paolo Baldan, Gianna Bell`e
Dipartimento di Matematica e Informatica,
via Zanon 6, 33100 Udine (Italy)
falessi,baldan,gbelleg@dimi.uniud.it
Abstract
Various results appear in the literature for deriving existence and
uniqueness of fixed points for endofunctors on categories of complete met­
ric spaces. All these results are proved for contracting functors which
satisfy some further requirements, depending on the category in question.
Following a new kind of approach, based on the notion of j­isometry,
we show that the sole hypothesis of contractivity is enough for proving
existence and uniqueness of fixed points for endofunctors on the category
of compact metric spaces and embedding­projection pairs.
1 Introduction
Categories of metric spaces have turned out to be very useful in giving de­
notational semantics to concurrent programming languages. The key idea is
the following: the longer the processes exhibit the same behaviour, the smaller
the distance between two processes is. In various papers (see e.g. [2], [3], [8],

  

Source: Alessi, Fabio - Dipartimento di Matematica e Informatica, Universitą degli Studi di Udine

 

Collections: Computer Technologies and Information Sciences