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On the order-theoretic Cantor theorem. (English) Zbl 0991.54035
Summary: In this report (presented at the 1999 International Conference on Nonlinear Analysis held in Taipei, October 16-20, 1999), we present an order-theoretic version of the Cantor theorem. This result, which is based on the interplay of the notions of partial order and of completeness, permits to give a unified and simplified account to a long list of results related to the Bishop-Phelps theorem. We survey briefly only its simplest applications and refer the reader to our forthcoming paper [Order-theoretic Cantor theorem and its applications] for a complete presentation of the results.

54E50Complete metric spaces
49J45Optimal control problems involving semicontinuity and convergence; relaxation
54H25Fixed-point and coincidence theorems in topological spaces