Abstract
In this paper we give a uniform way of proving cartesian closedness for many new subcategories of continuous posets. We define C-P to be the category of continuous posets whose D–completions are isomorphic to objects from C, where C is a subcategory of the category CONT of domains. The main result is that if C is a cartesian closed full subcategory of ALG ⊥ or BC, then C-P is also a cartesian closed subcategory of the category CONTP of continuous posets and Scott continuous functions. In particular, we have the following cartesian closed categories : BC-P, LAT-P, aL-P, aBC-P, B-P, aLAT-P, ω -B-P, ω -aLAT-P, etc.
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References
Jung, A.: Cartesian Closed Categories of Domains, volume 66 of CWI Tracts. Centrum voor Wiskunde en Informatica, Amsterdam (1989)
Normann, D.: On sequential functionals of type 3. Math. Struct. Comput. Sci. 16(2), 279–289 (2006)
Lawson, J., Xu, L.: Posets having continuous intervals. Theor. Comput. Sci. 316(1), 89–103 (2004)
Mao, X., Xu, L.: Quasicontinuity of posets via Scott topology and sobrification. Order 23(4), 359–369 (2006)
Xu, L.: Continuity of posets via Scott topology and sobrification. Topology and its Applications 153(11), 1886–1894 (2006)
Xu, L.: FS-Posets and continuous L-posets. Fuzzy Systems and Mathematics 18 (9), 124–127 (2004)
Mao, X., Xu, L.: B-posets, FS-posets and relevant categories. Semigroup Forum 72(1), 121–133 (2006)
Huang, M., Li, Q., Li, J.: Generalized continuous posets and a new cartesian closed category. Appl. Categ. Struct. 17(1), 29–42 (2009)
Zhao, D., Fan, T.: Dcpo-completion of posets. Theor. Comput. Sci. 411(22), 2167–2173 (2010)
Gierz, G., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislove, M., Scott, D. S.: Continuous Lattices and Domains, volume 93 of Encyclopedia of Mathematics and its Applications Cambridge University Press (2003)
Abramsky, S., Jung, A.: Domain theory. In: Abramsky, S., Gabbay, D. M., Maibaum, T. S. E. (eds.) Semantic Structures, volume 3 of Handbook of Logic in Computer Science, pp 1–168. Clarendon Press (1994)
Keimel, K., Lawson, J. D.: D-completions and the d-topology. Annals of Pure and Applied Logic 159(3), 292–306 (2009)
Jung, A., Moshier, M. A., Vickers, S. J.: Presenting dcpos and dcpo algebras. In: Bauer, A., Mislove, M. (eds.) Proceedings of the 24th Conference on the Mathematical Foundations of Programming Semantics, volume 218 of Electronic Notes in Theoretical Computer Science, pp 209–229. Elsevier Science Publishers (2008)
Zhao, D.: Closure spaces and completions of posets. Semigroup Forum 90(2), 545–555 (2015)
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Zhang, Z., Li, Q. & Jia, X. Cartesian Closed Extensions of Subcategories of CONT. Order 34, 513–521 (2017). https://doi.org/10.1007/s11083-016-9412-1
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DOI: https://doi.org/10.1007/s11083-016-9412-1