Stefan Sokolowski

POINT GLUEING IN CPO-S

863

Abstract

I came across the need to factor cpo-s while working on a homotopy theory of concurrent processes. I needed a ``natural'' cpo structure in the set of equivalence classes, along with a number of simple properties of that quotient cpo. To my surprise, I could not find this in the available literature. In this report, the reader will find the respective technical details worked out. They are in no technical way connected to my original motivation -- homotopies of processes -- and may be studied separately, as another small theory of abstract mathematical structures. But the computer science rationale guides my hand in telling the interesting from the uninteresting. The report will tell you how to factor partial orders to get partial orders; and how to factor cpo-s to get cpo-s; and how to ``collapse'' cpo-s to get simpler cpo-s.

Key words: collapse, concurrency, homotopy, algebraic topology.