On the Duality of Compact vs. Open

Annals of the New York Academy of Sciences

Volumn 806, Issue , 1996, Pages 214-230

  Jung, Achim ^a   Sünderhauf, Philipp ^b  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

(strong) proximity lattice; Coherent space; Stone duality

Indexed keywords

EID: 3142628487     PISSN: 00778923     EISSN: None     Source Type: Book Series    
DOI: 10.1111/j.1749-6632.1996.tb49171.x     Document Type: Article

References (15)

1. ABRAMSKY, S. & A. JUNG. 1994. Domain theory. In: Handbook of Logic in Computer Science (S. Abramsky, D. M. Gabbay, & T.S.E. Maibaum, Eds.). 3: 1-168. Clarendon Press.
2. DAVEY, B.A. & H. A. PRIESTLEY. 1990. Introduction to Lattices and Order. Cambridge University Press, Cambridge.
3. GIERZ, G., K.H. HOFMANN, K. KEIMEL, J.D. LAWSON, M. MISLOVE, & D.S. SCOTT. 1980. A Compendium of Continuous Lattices. Springer Verlag, New York.
4. GIERZ, G. & K. KEIMEL. 1981. Continuous ideal completions and compactifications. In: Continuous Lattices, Proceedings Bremen 1979 (B. Banaschewski and R.-E. Hoffmann, Eds.). Lecture Notes in Mathematics. 871: 97-124. Springer Verlag. New York.
5. HOFMANN, K.H. & M. MISLOVE. 1981. Local compactness and continuous lattices. In: Continuous Lattices, Proceedings Bremen 1979 (B. Banaschewski and R.-E. Hoffmann, Eds.). Lecture Notes in Mathematics. 871: 209-248. Springer Verlag. New York.
6. JOHNSTONE, P.T. 1982. Stone Spaces. Cambridge Studies in Advanced Mathematics, Vol. 3. Cambridge University Press. Cambridge.
7. KOPPERMAN, R. 1994. The skew-fields of topology. Manuscript.
8. KEIMEL, K. & J. PASEKA. A direct proof of the Hofmann-Mislove theorem. Proceedings of the Amer. Math. Soc. 120:301-303.
9. LAWSON, J.D. 1988. The versatile continuous order. In: Mathematical Foundations of Programming Language Semantics (M. Main, A. Melton, M. Mislove, & D. Schmidt, Eds.). Lecture Notes in Computer Science. 298: 134-160. Springer Verlag. New York.
10. LAWSON, J.D. 1991. Order and strongly sober compactification. In: Topology and Category Theory in Computer Science (G.M. Reed, A.W. Roscoe, & R.F. Wachter, Eds.). 179-205. Clarendon Press. Oxford.
11. NACHBIN, L. 1965. Topology and Order. Van Nostrand. Princeton, N.J. (Reprinted by Robert E. Kreiger Publ. Co. Huntington, NY. 1967.)
12. SMYTH, M.B. 1977. Effectively given domains. Theoretical Computer Science. 5: 257-274.
13. SMYTH, M.B. 1986. Finite approximation of spaces. In: Category Theory and Computer Programming (D. Pitt, S. Abramsky, A. Poigné, & D. Rydeheard, Eds.). Lecture Notes in Computer Science. 240: 225-241. Springer Verlag.
14. SMYTH, M.B. 1992. Stable compactification I. J. London Math. Soc. 45: 321-340.
15. STONE, M.H. 1936. The theory of representations for Boolean algebras. Trans. American Math. Soc. 40: 37-111.