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Two preservation results for countable products of sequential spaces

  • MATTHIAS SCHRÖDER (a1) and ALEX SIMPSON (a1)

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.

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Battenfeld, I. (2006) Modelling Computational Effects in QCB (in preparation).
Battenfeld, I., Schröder, M. and Simpson, A. K. (2005) Compactly generated domain theory. Mathematical Structures in Computer Science 16 141161.
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 105145.
Franklin, S. P. (1965) Spaces in which sequences suffice. Fundamenta Mathematicae 57 107115.
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.
Menni, M. and Simpson, A. K. (2002) Topological and limit space subcategories of countably-based equilogical spaces. Mathematical Structures in Computer Science 12 739770.
Plotkin, G. D. and Power, A. J. (2002) Computational effects and operations: An overview. Electronic Notes in Theoretical Computer Science 73 149163.
Schröder, M. (2002) Extended Admissibility. Theoretical Computer Science 284 519538.
Schröder, M. (2003) Admissible Representations for Continuous Computations, Ph.D. thesis, FernUniversität Hagen.
Simpson, A. K. (2003) Towards a convenient category of topological domains. In: Proceedings of thirteenth ALGI Workshop, RIMS, Kyoto University.
Stoltenberg-Hansen, V. and Tucker, J. V. (1995) Effective Algebras. In: Handbook of Logic in Computer Science 4, Oxford University Press 357526.
Weihrauch, K. (2000) Computable Analysis, Springer.
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 871384389.

Two preservation results for countable products of sequential spaces

  • MATTHIAS SCHRÖDER (a1) and ALEX SIMPSON (a1)

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