Brezis-Browder Principle Revisited
Abstract
En
Most of the known (sequential) maximality principles are logical equivalents of the Brezis-Browder’s [Adv. Math., 21 (1976), 355-364]. But, for at least one of these, the inclusional relation cannot be reversed. It is our aim to put this (metrical) statement in its natural (abstract) framework. Some applications of these facts to Zorn maximality principles are then given.
Most of the known (sequential) maximality principles are logical equivalents of the Brezis-Browder’s [Adv. Math., 21 (1976), 355-364]. But, for at least one of these, the inclusional relation cannot be reversed. It is our aim to put this (metrical) statement in its natural (abstract) framework. Some applications of these facts to Zorn maximality principles are then given.
DOI Code:
10.1285/i15900932v28n2p33
Keywords:
Quasi-order; maximal element; sequential inductivity; monotone function; pseudometric; Cauchy/asymptotic sequence; convergence structure; regularity
Classification:
49J53; 47J30
Full Text: PDF
