AC, the axiom of choice, because of its non-constructive
character, is the most controversial mathematical axiom. It is
shunned by some, used indiscriminately by others. This treatise
shows paradigmatically that disasters happen without AC and they
happen with AC. Illuminating examples are drawn from diverse areas
of mathematics, particularly from general topology, but also from
algebra, order theory, elementary analysis, measure theory, game
theory, and graph theory.
General
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