Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!sun-barr!olivea!mintaka!bloom-beacon!eru!hagbard!sunic!mcsun!ukc!mucs!m1!bevan From: bevan@cs.man.ac.uk (Stephen J Bevan) Newsgroups: comp.theory Subject: Novice question about monotonic/continuous functions Message-ID: Date: 16 Jun 91 17:01:08 GMT Sender: news@cs.man.ac.uk Distribution: comp Organization: Department of Computer Science, University of Manchester Lines: 26 I'm currently reading a book on category theory, and in the initial chapters it goes through some mathematical structures that can be represented as categories such as :- semigroups, monoids, posets, ... etc. I have read about these in various guises before (courses on algebra, denotational semantics), but never fully understood them (I'm a poor CS type not a mathematical person :-), but I thought that as they are appearing yet again, I'd make a more concerted effort. Anyway, my problem (for today :-) is that I can't think of a function on a CPO (complete partial order) that is monotonic but is _not_ continuous. (I once asked this question to the person teaching the denotational semantics course and was told `Er, um, see me next time') Now there must be some as every book I've read defines what a monotone function is and then goes on to define a continuous one. However, I've yet to see one that gives any decent examples! So, can anybody help me with my (hopefully simple) question and also point me at a book/report/paper that explains these sorts of things and actually has some examples to go along with the (dry) definitions! Stephen J. Bevan bevan@cs.man.ac.uk PS. Just in case anybody is wondering :- this is not home/course work