[1] Adámek, J., Herrlich, H., and Strecker, G.E., “Abstract and Concrete Categories:The joy of cats”, John Wiley & Sons Inc., 1990 (Republished in: Reprints in Theoryand Applications of Categories 17, 2006).
[2] Alexandroff, P., Diskrete Räume, Recueil Mathématique. Nouvelle Série 2 (1937),501-519.
[3] Banaschewski, B., Lowen, R., and Van Olmen, C., Sober approach spaces, TopologyAppl. 153(16) (2006), 3059–3070.
[4] Barr, M., Relational algebras, in S. MacLane et al. (eds), Reports of the MidwestCategory Seminar IV, Lecture Notes in Math. 137 (1970), 39-55.
[5] Bénabou, J., Distributors at work, Lecture notes written by Thomas Streicher(2000), 28 pages.
[6] Birkhoff, G., Moore–Smith convergence in general topology, Ann. of Math. 38(1)(1937), 39-56.
[7] Bonsangue, M.M., van Breugel, F., and Rutten, J., Generalized metric spaces: completion,topology, and powerdomains via the Yoneda embedding, Theoret. Comput.Sci. 193(1-2) (1998), 1-51.
[8] Bourbaki, N., “Éléments de Mathématique. 3. Pt. 1: Les structures fondamentalesde l’analyse. Livre 3: Topologie générale”, Paris: Hermann & Cie., 1942.
[9] Cartan, H., Filtres et ultrafiltres, Comptes Rendus Hebdomadaires des Séances del’Académie des Sciences 205 (1937), 777-779.
[10] Cartan, H., Théorie des filtres, Comptes Rendus Hebdomadaires des Séances del’Académie des Sciences 205 (1937), 595-598.
[11] Chai, Y.M., A note on the probabilistic quasi-metric spaces, J. Sichuan Univ. Nat.Sci. 46(3) (2009), 543-547.
[12] Chikhladze, D., Clementino, M.M., and Hofmann, D., Representable (T; V)-categories, Appl. Categ. Structures 23(6) (2015), 829-858 (eprint: www.mat.us.pt/preprints/ps/p1247.pdf).
[13] Clark, P.L., Convergence (2013), 29 pages (available at http://math.uga.edu/~pete/convergence.pdf).
[14] Clementino, M.M. and Hofmann, D., Topological features of lax algebras,Appl. Categ. Structures 11(3) (2003), 267-286 (eprint: http://www.mat.uc.pt/preprints/ps/p0109.ps).58 D. Hofmann and C. D. Reis
[15] Clementino, M.M. and Hofmann, D., Lawvere completeness in topology, Appl. Categ.Structures 17(2) (2009), 175-210 (arXiv:0704.3976 [math.CT]).
[16] Clementino, M.M. and Hofmann, D., The Rise and Fall of V -functors, Fuzzy Setsand Systems 321 (2017), 29-49 (eprint: http://www.mat.uc.pt/preprints/ps/p1606.pdf).
[17] Cook, C.H. and Fischer, H.R., Regular convergence spaces, Math. Ann. 174(1)(1967), 1-7.
[18] Cornish, W.H., On H. Priestley’s dual of the category of bounded distributive lattices,Mat. Vesnik New Series 12 (1975), 329-332.
[19] Flagg, R.C., Completeness in continuity spaces, Seely, R.A.G. (ed.), Category theory1991: Proceedings of an International Summer Category Theory Meeting, held inMontréal, Québec, Canada, June 23-30, 1991. Published by American MathematicalSociety for the Canadian Mathematical Society, CMS Conference Proceedings 13(1992) 183-199.
[20] Flagg, R.C., Quantales and continuity spaces, Algebra Universalis 37(3) (1997), 257-276.
[21] Flagg, R.C., Sünderhauf, P., and Wagner, K., A logical approach to quantitativedomain theory, Topology Atlas Preprint 23 (eprint: http://at.yorku.ca/e/a/p/p/23.htm).
[22] Fleisher, I., Priestley’s duality from Stone’s., Adv. in Appl. Math. 25(3) (2000),233-238.
[23] Fréchet, M.R., Généralisation d’un théorème de Weierstrass, Comptes Rendus Hebdomadairesdes Séances de l’Académie des Sciences 139 (1904), 848-850.
[24] Fréchet, M.R., Sur quelques points du calcul fonctionnel, Rend. Circ. Mat. Palermo(2) Suppl. 22(1) (1906), 1-74.
[25] Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M.W., and Scott,D.S., “A Compendium of Continuous Lattices”, Springer-Verlag, 1980.
[26] Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M.W., and Scott,D.S., “Continuous Lattices and Domains”, Encyclopedia of Mathematics and itsApplications 93, Cambridge University Press, 2003.
[27] Grimeisen, G., Gefilterte summation von filtern und iterierte grenzprozesse I, Math.Ann. 141(4) (1960), 318-342.
[28] Grimeisen, G., Gefilterte summation von filtern und iterierte grenzprozesse II, Math.Ann. 144(5) (1961), 386-417.Convergence and quantale-enriched categories 59
[29] Gutierres, G. and Hofmann, D., Approaching metric domains, Appl. Categ. Structures21(6) (2013), 617-650 ( arXiv:1103.4744 [math.GN]).
[30] Hausdorff, F., “Grundzüge der Mengenlehre”, Leipzig Verlag von Veit & Company,1914.
[31] Hausdorff, F., “Grundzüge der Mengenlehre”, Chelsea Publishing, 1965 (reprint offirst edition published in Berlin, 1914).
[32] Hermida, C., Representable multicategories, Adv. Math. 151(2) (2000), 164-225.
[33] Hermida, C., From coherent structures to universal properties, J. Pure Appl. Algebra165(1) (2001), 7-61.
[34] Hochster, M., Prime ideal structure in commutative rings, Trans. Amer. Math. Soc.142 (1969), 43-60.
[35] Hofmann, D., An algebraic description of regular epimorphisms in topology, J. PureAppl. Algebra 199(1-3) (2005), 71-86.
[36] Hofmann, D., Topological theories and closed objects, Adv. Math. 215(2) (2007),789-824.
[37] Hofmann, D., Duality for distributive spaces, Theory Appl. Categ. 28(3) (2013),66-122 (arXiv:1009.3892 [math.CT]).
[38] Hofmann, D., The enriched Vietoris monad on representable spaces, J. Pure Appl.Algebra 218(12) (2014), 2274-2318 (arXiv:1212.5539 [math.CT]).
[39] Hofmann, D. and Reis, C.D., Probabilistic metric spaces as enriched categories,Fuzzy Sets and Systems 210, (2013), 1-21 (arXiv:1201.1161 [math.GN]).
[40] Hofmann, D., Seal, G.J., and Tholen, W. (eds.), “Monoidal Topology. A CategoricalApproach to Order, Metric, and Topology”, Encyclopedia of Mathematics and itsApplications 153, Cambridge University Press, 2014.
[41] Hofmann, D. and Stubbe, I., Towards Stone duality for topological theories, TopologyAppl. 158(7) (2011), 913-925 (arXiv:1004.0160 [math.CT]).
[42] Hofmann, D. and Tholen, W., Lawvere completion and separation via closure, Appl.Categ. Structures 18(3) (2010), 259-287 (arXiv:0801.0199 [math.CT]).
[43] Hofmann, D. and Waszkiewicz, P., A duality of quantale-enriched categories, J. PureAppl. Algebra 216(8-9) (2012), 1866-1878 (arXiv:1012.3351 [math.CT]).
[44] Johnstone, P.T., “Stone spaces”, Cambridge Studies in Advanced Mathematics 3,Cambridge University Press, 1986 (reprint of the 1982 edition).60 D. Hofmann and C. D. Reis
[45] Jung, A., Stably compact spaces and the probabilistic powerspace construction, Electron.Notes Theor. Comput. Sci. 87 (2004), 5-20
[46] Kelly, G.M., “Basic concepts of enriched category theory”, London Math. Soc. LectureNote Ser. 64 (1982) (Republished in: Repr. Theory Appl. Categ. 10 (2005),1-136).
[47] Kelly, G.M. and Schmitt, V., Notes on enriched categories with colimits of someclass, Theory Appl. Categ. 14(17) (2005), 399-423.
[48] Lai, H. and Tholen, W., Quantale-valued approach spaces via closure and convergence,Tech. rep. (2016) (arXiv:1604.08813 [math.GN]).
[49] Lawson, J., Stably compact spaces, Math. Structures Comput. Sci. 21(1) (2011),125-169.
[50] Lawvere, F.W., Metric spaces, generalized logic, and closed categories, Rendicontidel Seminario Matemàtico e Fisico di Milano, 43(1) (1973), 135-166 (Republishedin: Repr. Theory Appl. Categ. 1 (2002), 1-37).
[51] Li, W. and Zhang, D., Sober metric approach spaces, Tech. rep. (2016)(arXiv:1607.03208 [math.GN]).
[52] Lowen, R., Approach spaces: a common supercategory of TOP and MET, Math.Nachr. 141(1) (1989), 183-226.
[53] Lowen, R., “Approach spaces: The missing link in the topology-uniformity-metrictriad”, The Clarendon Press, 1997, Oxford Science Publications, 1997.
[54] MacDonald, J. and Sobral, M., Aspects of Monads, In: Pedicchio, M.C. and Tholen,W., Categorical Foundations: Special Topics in Order, Topology, Algebra, and SheafTheory, Encyclopedia of Mathematics and its Applications 97, Cambridge UniversityPress (2004), 213-268.
[55] Manes, E.G., A triple theoretic construction of compact algebras, In: B. Eckmann(ed.), Seminar on Triples and Categorical Homology Theory, Lecture Notes in Math.80 (1969), 91-118.
[56] Menger, K., Statistical metrics, Proc. Natl. Acad. Sci. 28 (1942), 535-537.
[57] Moore, E.H., Definition of limit in general integral analysis, Nat. Acad. Proc. 1(12)(1915), 628-632.
[58] Moore, E.H. and Smith, H.L., A General Theory of Limits, Amer. J. Math. 44(2)(1922), 102-121.
[59] Nachbin, L., “Topologia e Ordem”, University of Chicago Press, 1950.Convergence and quantale-enriched categories 61
[60] Pedicchio, M.C. and Tholen, W. (eds.), “Categorical Foundations: Special Topics inOrder, Topology, Algebra, and Sheaf Theory”, Encyclopedia of Mathematics and itsApplications 97, Cambridge University Press, 2004.
[61] Priestley, H.A., Representation of distributive lattices by means of ordered stonespaces, Bull. London Math. Soc. 2(2) (1970), 186-190.
[62] Priestley, H.A., Ordered topological spaces and the representation of distributive lattices,Proc. London Math. Soc. (3), 24(3) (1972), 507-530.
[63] Pumplün, D., Eine Bemerkung über Monaden und adjungierte Funktoren, Math.Ann. 185(4) (1970), 329-337.
[64] Raney, G.N., Completely distributive complete lattices, Proc. Amer. Math. Soc. 3(5)(1952), 677-680.
[65] Rosenthal, K.I., “The Theory of Quantaloids”, CRC Press, 1996.
[66] Rutten, J., Elements of generalized ultrametric domain theory, Theoret. Comput.Sci. 170(1-2) (1996), 349-381.
[67] Schweizer, B. and Sklar, A., “Probabilistic metric spaces”, North-Holland Series inProbability and Applied Mathematics, North-Holland Publishing Co., 1983.
[68] Scott, D., Continuous lattices, In: Lawvere F.W. (eds) Toposes, Algebraic Geometryand Logic, Lecture Notes in Math. 274 (1972), 97-136.
[69] Smyth, M.B., Quasi-uniformities: Reconciling domains with metric spaces, In: MainM., Melton A., Mislove M., Schmidt D. (eds) Mathematical Foundations of ProgrammingLanguage Semantics, MFPS 1987, Lecture Notes in Computer Sci. 298 (1988),236-253.
[70] Stone, M.H., Topological representations of distributive lattices and Brouwerianlogics, Casopis pro pestování matematiky a fysiky 67(1) (1938), 1-25 (eprint:http://dml.cz/handle/10338.dmlcz/124080).
[71] Stubbe, I., An introduction to quantaloid-enriched categories, Fuzzy Sets and Systems256 (2014), 95-116 (Special issue on Enriched Category Theory and RelatedTopics, Selected papers from the 33rd Linz Seminar on Fuzzy Set Theory, 2012).
[72] Tholen, W., Ordered topological structures, Topology Appl. 156(12) (2009), 2148-2157.
[73] Van Olmen, C., “A study of the interaction between frame theory and approach”theory, PhD Thesis, University of Antwerp, 2005.
[74] Vickers, S., Localic completion of generalized metric spaces I, Theory Appl. Categ.14(15) (2005), 328-356.62 D. Hofmann and C. D. Reis
[75] Wagner, K.R., “Solving recursive domain equations with enriched categories”, PhDThesis, Carnegie Mellon University, 1994 (eprint: ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1994/94-62.ps.gz).
[76] Wagner, K.R., Liminf convergence in !-categories, Theoret. Comput. Sci. 184(1-2)(1997), 61-104.
[77] Waszkiewicz, P., On domain theory over Girard quantales, Fundamenta Informaticæ92(1-2) (2009), 169-192.
[78] Wood, R.J., Ordered sets via adjunction, In: Pedicchio, M.C. and Tholen, W. (eds.),“Categorical Foundations: Special Topics in Order, Topology, Algebra, and SheafTheory”, Encyclopedia of Mathematics and its Applications 97, Cambridge UniversityPress (2004), 5-47.
[79] Wyler, O., Convergence axioms for topology, Ann. New York Acad. Sci. 806(1)(1996), 465-475.
[80] Yetter, D.N., Quantales and (noncommutative) linear logic, J. Symbolic Logic 55(1)(1990), 41-64.