On the Order-theoretic Cantor Theorem of Granas and Horvath
Keywords:
Cantor theorem, fixed point theorem, pre-order, metric space, fixed point, stationary point, maximal elementAbstract
In 2000, Granas and Horvath published an order-theoretic version of the Cantor theorem based on the interplay of the notions of partial order and of completeness. This result gave a unified and simplified account to a long list of results related to the Bishop-Phelps theorem. In the present article, we obtain characterizations of their Cantor type theorem, that is, its equivalent formulations to maximality theorem, various types of collectively fixed point theorems and collectively stationary point theorems. We are based on our 2023 Metatheorem in the ordered fixed point theory and the Brøndsted-Jachymski principle recently due to ourselves.References
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