Towards a Convenient Category of Topological Domains (Algebra, Logic and Geometry in Informatics)
Year: 2003
Type: article
Abstract: We propose acategory of topological spaces that promises to be convenient for the purposes of domain theory as amathematical the- ory for modelling computation.Our notion of convenience presupposes the usual properties of domain theory, e.g.$\mathrm{m}\mathrm{o}\mathrm{d} \dot{\mathrm{e}}\mathrm{U}\mathrm{i}\mathrm{n}\mathrm{g}$ the basic type constructors, fixed points, recursive types, etc.In addition, we seek to model parametric polymorphism, and also to provide aflexible toolkit for modelling computational effects as free algebras for algebraic theories.Our convenient category is obtained as an application of recent work on the remarkable closure conditions of the category of quotients of countably-based topological spaces.Its convenience is aconsequence of aconnection with realizability models. 1IntroductionThe title of this note deliberately echoes that of Steenrod's well-known paper: A Convenient Category of Topological Spaces,[46].In his paper, Steen- rod sets out to find afull subcategory of the category Top of all topological spaces that is "convenient" for the purposes of algebraic topology.One aspect of "convenience" that is particularly highlighted by Steenrod is carte sian closure, aproperty famously not enjoyed by Top itself.He argues at length that the category of compactly-generated Hausdorff spaces, which is cartesian closed, does provide all the "conveniences" needed for doing algebraic topology.
Source: 数理解析研究所講究録
Author: Alex Simpson
Language: English
Subfield: Software
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2171974074