[At] Atsuji M.: 
Uniform continuity of continuous functions of metric spaces. Pacific J. Math. 8 (1958), 11-16. 
MR 0099023 | 
Zbl 0082.16207[AW] Attouch H., Wets R.: 
Quantitative stability of variational systems I, The epigraphical distances. preprint. 
MR 1018570[ALW] Attouch H., Lucchetti R., Wets R.: 
The topology of the $\rho $-Hausdorff distance. to appear in Annali Mat. Pure Appl. 
Zbl 0769.54009[AP] Aze D., Penot J.: 
Operations on convergent families of sets and functions. Optimization 21 (1990), 521-534. 
MR 1069660 | 
Zbl 0719.49013[Be] Beer G.: 
Metric spaces on which continuous functions are uniformly continuous and Hausdorff distance. Proc. Amer. Math. Soc. 95 (1985), 653-658. 
MR 0810180 | 
Zbl 0594.54007[BDC1] Beer G., DiConcilio A.: 
A generalization of boundedly compact metric spaces. Comment. Math. Univ. Carolinae 32 (1991), 362-367. 
MR 1137797[BDC2] Beer G., DiConcilio A.: 
Uniform continuity on bounded sets and the Attouch-Wets topology. Proc. Amer. Math. Soc. 112 (1991), 235-244. 
MR 1033956[BL1] Beer G., Lucchetti R.: 
Weak topologies for the closed subsets of a metrizable space. to appear in Trans. Amer. Math. Soc. 
MR 1094552 | 
Zbl 0810.54011[BL2] Beer G., Lucchetti R.: 
Well-posed optimization problems and a new topology for the closed subsets of a metric space. preprint. 
MR 1256444 | 
Zbl 0812.54015[BLLN] Beer G., Lechicki A., Levi S., Naimpally S.: Distance functionals and the suprema of hyperspace topologies. to appear in Annali Mat. Pure Appl.
[Ho] Holá Ł.: 
The Attouch-Wets topology and a characterization of normable linear spaces. Bull. Austral. Math. Soc. 44 (1991), 11-18. 
MR 1120389[LL] Lechicki A., Levi S.: 
Wijsman convergence in the hyperspace of a metric space. Bull. Un. Mat. Ital. 5-B (1987), 435-452. 
MR 0896334 | 
Zbl 0655.54007[Pe] Penot J.P.: 
The cosmic Hausdorff topology, the bounded Hausdorff topology, and continuity of polarity. to appear in Proc. Amer. Math. Soc. 
MR 1068129 | 
Zbl 0774.54008