Order Isomorphic
المؤلف:
Ciesielski, K.
المصدر:
et Theory for the Working Mathematician. Cambridge, England: Cambridge University Press, 1997.
الجزء والصفحة:
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5-1-2022
1672
Order Isomorphic
Two totally ordered sets 
and 
are order isomorphic iff there is a bijection 
from 
to 
such that for all 
,
(Ciesielski 1997, p. 38). In other words, 
and 
are equipollent ("the same size") and there is an order preserving mapping between the two.
Dauben (1990) and Suppes (1972) call this property "similar." The definition works equally well on partially ordered sets.
REFERENCES:
Ciesielski, K. Set Theory for the Working Mathematician. Cambridge, England: Cambridge University Press, 1997.
Dauben, J. W. Georg Cantor: His Mathematics and Philosophy of the Infinite. Princeton, NJ: Princeton University Press, 1990.
Mansour, T. "Permutations Avoiding a Pattern from 
and at Least Two Patterns from 
." 31 Jul 2000. http://arxiv.org/abs/math.CO/0007194.
Suppes, P. Axiomatic Set Theory. New York: Dover, 1972.
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