Mathematical Structures in Computer Science

Paper

Two preservation results for countable products of sequential spaces

MATTHIAS SCHRÖDERa1 and ALEX SIMPSONa1

a1 LFCS, School of Informatics, University of Edinburgh, U.K. Email: mschrode@inf.ed.ac.uk, alex.simpson@ed.ac.uk

Abstract

We prove two results for the sequential topology on countable products of sequential topological spaces. First we show that a countable product of topological quotients yields a quotient map between the product spaces. Then we show that the reflection from sequential spaces to its subcategory of monotone ω-convergence spaces preserves countable products. These results are motivated by applications to the modelling of computation on non-discrete spaces.

(Received December 15 2006)

(Revised April 26 2006)