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Recent hypertopologies and continuity of the value function and of the constrained level sets |
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| Authors: | R. Lucchetti P. Shunmugaraj Y. Sonntag |
| Affiliation: | 1. Dip. di Matematica , Via Saldini 50, Milano, 20133, Italy;2. LMC IMAG , Université J. Fourier , Grenoble, 38041, France;3. Université de Provence , Case X, 3 PL V. Hugo, 13331 Marseille, France |
| Abstract: | Given a continuous function f: X→R, sufficient conditions are offered for the continuity of the value function v(A):=inf{f{x): x ε A} and of the level set multifunction Lev(A, α) := {x ε A: f(x)?α}, with respect to recently defined topologies on the closed sets of a metric space. |
| Keywords: | proximal and bounded proximal topologies slice topology value function constrained level set approximated solution set AMS subject numbers: 49A50 49B50 54B20 |