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Pseudometric and cardinal extensions of the Brézis-Browder ordering principle. (English) Zbl 0686.04004

The Brézis-Browder ordering principle can be stated as follows: Let X be a quasi-ordering such that each ascending sequence has an upper bound, and let \(\phi\) be a function which is decreasing and bounded from below. Then for each \(x\in X\) there is a \(\phi\)-maximal point z with \(x\leq z.\)
The author generalizes this principle to (a) pseudo-metrics on X and (b) families of functions \(\{\phi_ i:\) \(i\in M\}\) on X.
Reviewer: M.Weese

MSC:

03E25 Axiom of choice and related propositions
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