Bornological Convergences on the Hyperspace of a Uniformizable Space

Atkin, C.J.: Boundedness in uniform spaces, topological groups, and homogeneous spaces. Acta. Math. Hungar. 57(3-4), 213–232 (1991) Attouch, H., Wets, R.J.B.: A convergence theory for saddle functions. Trans. Amer. Math. Soc. 280(1), 1–41 (1983) Attouch, H., Wets, R.J.B.: Isometries for the Legendre-Fenchel transform. Trans. Amer. Math. Soc. 296(1), 33–60 (1986) Beer, G.: Topologies on Closed and Closed Convex Sets. Kluwer, Dodrecht (1993) Beer, G.: Operator topologies and graph convergence. J. Convex Anal. 16(3-4), 687–698 (2009) Beer, G.: The Alexandroff property and the preservation of strong uniform continuity. Appl. Gen. Topol. 11(2), 117–133 (2010) Beer, G., Costantini, C., Levi, S.: Bornological convergence and shields. Mediterr. J. Math. 10(1), 529–560 (2013) Beer, G., Di Concilio, A.: Uniform continuity on bounded sets and the Attouch–Wets topology. Proc. Amer. Math. Soc. 112(1), 235–243 (1991) Beer, G., Garrido, M.I.: Bornologies and locally Lipschitz functions. Bull. Aust. Math. Soc. 90(2), 257–263 (2014) Beer, G., Garrido, M.I.: Locally Lipschitz functions, cofinal completeness, and UC spaces. J. Math. Anal. Appl. 428(2), 804–816 (2015) Beer, G., Levi, S.: Pseudometrizable bornological convergence is Attouch–Wets convergence. J. Convex Anal. 15(2), 439–453 (2008) Beer, G., Levi, S.: Strong uniform continuity. J. Math. Anal. Appl. 350(2), 568–589 (2009) Beer, G., Levi, S.: Uniform continuity, uniform convergence, and shields. Set-Valued Var. Anal. 18(3-4), 251–275 (2010) Beer, G., Lucchetti, R.: Weak topologies for the closed subsets of a metrizable space. Trans. Amer. Math. Soc. 335(2), 805–822 (1993) Beer, G., Lucchetti, R.: Well-posed optimization problems and a new topology for the closed subsets of a metric space. Rocky Mountain . J. Math. 23(4), 1197–1220 (1993) Bourbaki, N.: Elements of mathematics. General topology, vol. Part 1. Hermann, Paris (1966) Burton, M.H.: Boundedness in uniform spaces and fuzzy uniform spaces. Fuzzy Sets Syst. 58(2), 195–207 (1993) Di Concilio, A., Guadagni, C.: Bornological convergences and local proximity spaces. Topology Appl. 173, 294–307 (2014) Dolecki, S.: An initiation into convergence theory. In: Beyond topology, Contemp. Math., vol. 486 pp. 115–161. Amer. Math. Soc., Providence, RI (2009) Führ, H., Roelcke, W.: Contributions to the theory of boundedness in uniform spaces and topological groups. Note Mat. 16(2), 189–226 (1998). 1996 Garrido, M.I., Meroño, A.S.: New types of completeness in metric spaces. Ann. Acad. Sci. Fenn. Math. 39(2), 733–758 (2014) Hejcman, J.: Boundedness in uniform spaces and topological groups. Czechoslovak Math. J. 9(84), 544–563 (1959) Hogbe-Nlend, H.: Bornologies and functional analysis. North-Holland Publishing Co., Amsterdam-New York-Oxford (1977) Isbell, J.R.: Insufficiency of the hyperspace. Proc. Cambridge Philos. Soc. 62, 685–686 (1966) Klein, E., Thompson, A.: Theory of Correspondences. Wiley, New York (1984) Lechicki, A., Levi, S., Spakowski, A.: Bornological convergences. J. Math. Anal. Appl. 297(2), 751–770 (2004). Special issue dedicated to John Horváth Mosco, U.: Convergence of convex sets and of solutions of variational inequalities. Advances in Math. 3, 510–585 (1969) Murdeshwar, M.G., Theckedath, K.K.: Boundedness in a quasi-uniform space. Canad. Math. Bull. 13, 367–370 (1970) Pu, H.W., Pu, H.H.: Semi-quasi-uniform spaces. Portugal. Math. 33, 177–184 (1974) Rodríguez-López, J., Sánchez-Granero: Some properties of bornological convergences. Topology Appl. 158(1), 101–117 (2011) Rosa, M., Vitolo, P.: A question related to the Isbell problem. Topology Appl. 160(13), 1829–1848 (2013) Rosa, M., Vitolo, P.: Comparability of lower Attouch–Wets topologies. Filomat (2015). To appear Vroegrijk, T.: Uniformizable and realcompact bornological universes. Appl. Gen. Topol. 10(2), 277–287 (2009) Vroegrijk, T.: On the semi-uniformity of bornological convergence. Quaest. Math. 38(2), 285–296 (2015) Willard, S.: General topology. Addison-Wesley Publishing Co., Reading Mass (1970)