Complete Lattice
المؤلف:
Birkhoff, G
المصدر:
Lattice Theory, 3rd ed. Providence, RI: Amer. Math. Soc., 1967.
الجزء والصفحة:
...
5-1-2022
1471
Complete Lattice
A partially ordered set (or ordered set or poset for short) 
is called a complete lattice if every subset 
of 
has a least upper bound (supremum, 
) and a greatest lower bound (infimum, 
) in 
.
Taking 
shows that every complete lattice 
has a greatest element (maximum, 
) and a least element (minimum, 
).
Of course, every complete lattice is a lattice. Moreover, every lattice 
with a finite set 
is a complete lattice.
REFERENCES:
Birkhoff, G. Lattice Theory, 3rd ed. Providence, RI: Amer. Math. Soc., 1967.
Grätzer, G. General Lattice Theory, 2nd ed. Boston, MA: Birkhäuser, 1998.
الاكثر قراءة في نظرية المجموعات
اخر الاخبار
اخبار العتبة العباسية المقدسة
