Two preservation results for countable products of sequential spaces

Authors:
Matthias Schröder;Alex Simpson
Affiliations:
LFCS, School of Informatics, University of Edinburgh, U.K. Email: mschrode@inf.ed.ac.uk, alex.simpson@ed.ac.uk;LFCS, School of Informatics, University of Edinburgh, U.K. Email: mschrode@inf.ed.ac.uk, alex.simpson@ed.ac.uk
Venue:
Mathematical Structures in Computer Science
Year:
2007

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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.