In mathematics, apantachy orpantachie (from the Greek word πανταχη meaning everywhere) is a maximal totally orderedsubset of apartially ordered set, especially a set of equivalence classes of sequences of real numbers. The term was introduced bydu Bois-Reymond (1879,1882) to mean adense subset of an ordered set, and he also introduced "infinitary pantachies" to mean the ordered set of equivalence classes of real functions ordered by domination, but asFelix Hausdorff pointed out this is not a totally ordered set.[1]Hausdorff (1907) redefined a pantachy to be a maximal totally ordered subset of this set.
Hausdorff (1907), "Untersuchungen über Ordnungstypen IV, V",Ber. über die Verhandlungen der Königl. Sächs. Ges. Der Wiss. Zu Leipzig. Math.-phys. Klasse,59:84–159 English translation inHausdorff (2005)
