A General Principle on Ordered Sets in Nonlinear Functional Analysis
نویسنده
چکیده
We put forward in the present paper a general and very simple principle concerning order relations which unifies a number of diverse results in nonlinear functional analysis. These results include the normal solvability theorems, generalizations of the Bishop-Phelps theorem, invariance theorems for closed sets under flows in metric spaces, and a number of other new related results. It had been realized earlier that there were mutual interrelations between such theorems and vague similarities in their method of proof. Our discussion exhibits their mutual relation in an explicit way and derives them from a relatively transparent general argument.
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