Hostname: page-component-669899f699-swprf Total loading time: 0 Render date: 2025-04-25T20:38:03.808Z Has data issue: false hasContentIssue false
  • English
  • Français

Two preservation results for countable products of sequential spaces

Published online by Cambridge University Press:  01 February 2007

MATTHIAS SCHRÖDER  and
ALEX SIMPSON
MATTHIAS SCHRÖDER
Affiliation:
LFCS, School of Informatics, University of Edinburgh, U.K. Email: [email protected], [email protected]
ALEX SIMPSON
Affiliation:
LFCS, School of Informatics, University of Edinburgh, U.K. Email: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 17 , Issue 1 , February 2007 , pp. 161 - 172
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Battenfeld, I. (2006) Modelling Computational Effects in QCB (in preparation).Google Scholar
Battenfeld, I., Schröder, M. and Simpson, A. K. (2005) Compactly generated domain theory. Mathematical Structures in Computer Science 16 141–161.CrossRefGoogle Scholar
Escardó, M. H., Lawson, J. D. and Simpson, A. K. (2004) Comparing cartesian closed categories of core compactly generated spaces. Topology and its Applications 143 105–145.CrossRefGoogle Scholar
Franklin, S. P. (1965) Spaces in which sequences suffice. Fundamenta Mathematicae 57 107–115.Google Scholar
Gierz, G., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislove, M. W. and Scott, D. S. (2003) Continuous Lattices and Domains, Encyclopedia of Mathematics and its Applications, 93Cambridge University Press.CrossRefGoogle Scholar
Menni, M. and Simpson, A. K. (2002) Topological and limit space subcategories of countably-based equilogical spaces. Mathematical Structures in Computer Science 12 739–770.CrossRefGoogle Scholar
Plotkin, G. D. and Power, A. J. (2002) Computational effects and operations: An overview. Electronic Notes in Theoretical Computer Science 73 149–163.CrossRefGoogle Scholar
Schröder, M. (2002) Extended Admissibility. Theoretical Computer Science 284 519–538.CrossRefGoogle Scholar
Schröder, M. (2003) Admissible Representations for Continuous Computations, Ph.D. thesis, FernUniversität Hagen.Google Scholar
Simpson, A. K. (2003) Towards a convenient category of topological domains. In: Proceedings of thirteenth ALGI Workshop, RIMS, Kyoto University.Google Scholar
Stoltenberg-Hansen, V. and Tucker, J. V. (1995) Effective Algebras. In: Handbook of Logic in Computer Science 4, Oxford University Press 357–526.CrossRefGoogle Scholar
Weihrauch, K. (2000) Computable Analysis, Springer.CrossRefGoogle Scholar
Wyler, O. (1981) Dedekind complete posets and scott topologies. In: Continuous Lattices, Proceedings of the Conference on Topological and Categorical Aspects of Continuous Lattices, Bremen 1979. Springer-Verlag Lecture Notes in Mathematics 871384–389.Google Scholar