Comparing Cartesian closed categories of (core) compactly generated spaces

Topology and its Applications

Volumn 143, Issue 1-3, 2004, Pages 105-145

  Escardó, Martín ^a   Lawson, Jimmie ^b   Simpson, Alex ^c  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

^b LOUISIANA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

Cartesian closed category; Compactly generated space; Core compact space; Countably based space; Domain theory; Function space; Isbell topology; K space; Quotient space

Indexed keywords

EID: 4243171361     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2004.02.011     Document Type: Article

References (35)

1. Barr M. Building closed categories Cahiers Topologie Géom. Différentielle 19 2 1978 115-1290
2. Bauer A. A relationship between equilogical spaces and type two effectivity Dagstuhl Seminar on Computability and Complexity in Analysis, 2001 Math. Logic Quart. 48 suppl. 1 2002 1-15
3. A. Bauer, L. Birkedal, D.S. Scott, Equilogical spaces, Theoret. Comput. Sci., in press
4. Borceux F. Categories and structures Handbook of Categorical Algebra vol. 2 1994 Cambridge University Press Cambridge
5. R. Brown, Some problems of algebraic topology: A study of function spaces, function complexes and fd-complexes, Ph.D. Thesis, New College, Oxford University, December 1961
6. Brown R. Function spaces and product topologies Quart. J. Math. Oxford Ser. (2) 15 1964 238-250
7. Brown R. A Geometric Account of General Topology, Homotopy Types and the Fundamental Groupoid Topology second ed. 1988 Ellis Horwood Chichester
8. Day B.J. A reflection theorem for closed categories J. Pure Appl. Algebra 2 1 1972 1-11
9. Day B.J. Kelly G.M. On topological quotient maps preserved by pullbacks or products Proc. Cambridge Philos. Soc. 67 1970 553-558
10. Dolecki S. Greco G.H. Lechicki A. When do the upper Kuratowski topology (homeomorphically, Scott topology) and the co-compact topology coincide? Trans. Amer. Math. Soc. 347 1995 2869-2884
11. Dugundji J. Topology 1966 Allyn and Bacon Boston
12. M.H. Escardó, Topology of data types and computability concepts, Electronic Notes in Theoretical Computer Science, in press
13. Escardó M.H. Heckmann R. Topologies on spaces of continuous functions Topology Proc. 26 2 2001-2002 545-564
14. Gale D. Compact sets of functions and function rings Proc. Amer. Math. Soc. 1 1950 303-308
15. Gierz G. Hofmann K.H. Keimel K. Lawson J.D. Mislove M. Scott D.S. Continuous Lattices and Domains 2003 Cambridge University Press Cambridge
16. Hofmann K.H. Lawson J.D. On the order-theoretical foundation of a theory of quasicompactly generated spaces without separation axiom J. Austral. Math. Soc. Ser. A 36 2 1984 194-212
17. Hyland J.M.E. Filter spaces and continuous functionals Ann. of Math. Logic 16 1977 101-143
18. Isbell J. Function spaces and adjoints Math. Scand. 36 1975 317-339
19. Isbell J. General function spaces, products and continuous lattices Math. Proc. Cambridge Philos. Soc. 100 1986 193-205
20. Isbell J. A distinguishing example in k-spaces Proc. Amer. Math. Soc. 100 1987 593-594
21. Kelley J.L. General Topology 1955 Van Nostrand New York
22. Mac Lane S. Categories for the Working Mathematician 1971 Springer Berlin
23. Markowsky G. Chain-complete posets and directed sets with applications Algebra Universalis 6 1976 53-68
24. Menni M. Simpson A. Topological and limit-space subcategories of countably-based equilogical spaces Math. Structures Comput. Sci. 12 6 2002 739-770
25. 0-spaces J. Math. Mech. 15 1966 983-1002
26. Normann D. Recursion on the Countable Functionals Lecture Notes in Math. vol. 811 1980 Springer Berlin
27. M. Schröder, Admissible representations for continuous computations, Ph.D. Thesis, Universität Hagen, 2002
28. Schröder M. Extended admissibility Theoret. Comput. Sci. 284 2 2002 519-538
29. Schwarz F. Powers and exponential objects in initially structured categories and applications to categories of limit spaces Quaestiones Math. 6 1983 227-254
30. Schwarz F. Weck S. Scott topology, Isbell topology and continuous convergence, In: Hoffmann R.-E. Hofmann K.H. Continuous Lattices and Their Applications, Bremen, 1982, New York Lecture Notes in Pure Appl. Math. vol. 101 1985 251-273 Marcel Dekker New York
31. A. Simpson, Towards a convenient category of topological domains, in: Proceedings of 13th ALGI Workshop, RIMS, Kyoto University, 2003
32. Spanier E. Infinite symmetric products, function spaces, and duality Ann. of Math. (2) 69 1959 142-198
33. Steenrod N.E. A convenient category of topological spaces Michigan Math. J. 14 1967 133-152
34. Vogt R.M. Convenient categories of topological spaces for homotopy theory Arch. Math. (Basel) 22 1971 545-555
35. S. Weingram, Bundles, realizations and k-spaces, Ph.D. Thesis, Princeton University, 1961