 
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],
