Necessary condition of Criticality.

In the work is proved a theorem about of the necessary condition of criticality of the continuous mapping defined on the quasiconvex filter. This theorem is a central result of R. Gamkrelidze and G. Kharatishvili extremal problems theory. By this theory, as rule, investigation of the optimal problems are reduced on the finding necessary condition of criticality. From the necessary condition of criticality follows necessary optimality conditions for the optimal problem.

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