Page 229 - Textos de Matemática Vol. 46
P. 229

ESAKIA SPACES VIA IDEMPOTENT SPLIT COMPLETION 219
[22] Halmos, P. R. (1956), Algebraic logic. I. Monadic Boolean algebras, Compositio Math. 12, 217–249.
[23] Hochster, M. (1969), Prime ideal structure in commutative rings, Trans. Amer. Math. Soc. 142, 43–60.
[24] Hofmann, D. (2013), A four for the price of one duality principle for distributive spaces, Order 30 (2), 643–655.
[25] Hofmann, D. (2014), The enriched Vietoris monad on representable spaces, J. Pure Appl. Algebra 218 (12), 2274–2318.
[26] Johnstone, P. T. (1986), Stone spaces, volume 3 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, xxii+370 pages, reprint of the 1982 edition.
[27] Jung, A. (2004), Stably compact spaces and the probabilistic powerspace construction, in J. Desharnais and P. Panangaden, editors, Domain-theoretic Methods in Probabilistic Processes, volume 87, 15pp.
[28] Jung, A., Kegelmann, M. and Moshier, M. A. (2001), Stably compact spaces and closed relations, in Papers from the 17th conference on the mathematical foundations of pro- gramming semantics, (Aarhus University, Aarhus, Denmark, May 23–26, 2001), Elsevier, Electron. Notes Theor. Comput. Sci. volume 45, pages 209–231.
[29] Kock, A. (1995), Monads for which structures are adjoint to units, J. Pure Appl. Algebra 104 (1), 41–59.
[30] McKinsey, J. and Tarski, A. (1946), On closed elements in closure algebras, Ann. Math. (2) 47, 122–162.
[31] Nachbin, L. (1950), Topologia e Ordem, Univ. of Chicago Press, in Portuguese, English translation: Topology and Order, Van Nostrand, Princeton (1965).
[32] Priestley, H. A. (1970), Representation of distributive lattices by means of ordered stone spaces, Bull. London Math. Soc. 2, 186–190.
[33] Priestley, H. A. (1972), Ordered topological spaces and the representation of distributive lattices, Proc. London Math. Soc. (3) 24, 507–530.
[34] Pultr, A. and Sichler, J. (1988), Frames in Priestley’s duality, Cah. Topol. G´eom. Di↵´er. Cat´eg. 29 (3), 193–202.
[35] Rosebrugh, R. and Wood, R. J. (1994), Constructive complete distributivity IV, Appl. Categ. Structures 2 (2), 119–144.
[36] Rosebrugh, R. and Wood, R. J. (2004), Split structures, Theory Appl. Categ. 13, No. 12, 172–183.
[37] Sambin, G. and Vaccaro, V. (1988), Topology and duality in modal logic, Ann. Pure Appl. Logic 37 (3), 249–296.
[38] Schalk, A. (1993), Algebras for Generalized Power Constructions, Ph.D. thesis, Tech- nische Hochschule Darmstadt.
[39] Scott, D. (1972), Continuous lattices, in Toposes, algebraic geometry and logic (Conf., Dalhousie Univ., Halifax, N. S., 1971), Springer, Lect. Notes Math. volume 274, pages 97–136.
[40] Simmons, H. (1980), Reticulated rings, J. Algebra 66, 169–192.
[41] Simmons, H. (1982), A couple of triples, Topology Appl. 13 (2), 201–223.
[42] Stone, M. H. (1936), The theory of representations for Boolean algebras, Trans. Amer.
Math. Soc. 40 (1), 37–111.
[43] Stone, M. H. (1938), Topological representations of distributive lattices and Brouwerian
logics, Cˇasopis pro pˇestov´an´ı matematiky a fysiky 67 (1), 1–25.
[44] Vietoris, L. (1922), Bereiche zweiter Ordnung, Monatsh. Math. Phys. 32 (1), 258–280.









































































   227   228   229   230   231