All Retraction Operators on a Complete Lattice Form a Complete Lattice

Authors
Boyu, Li
Citation
Boyu, Li, All Retraction Operators on a Complete Lattice Form a Complete Lattice, Acta Mathematica Sinica, New Series Chinese Journal of Mathematics, 7(3), 1991, pp. 247-251
Journal title
Acta Mathematica Sinica, New Series Chinese Journal of Mathematics → ACNP
ISSN journal
10009574
Volume
7
Issue
3
Year of publication
1991
Pages
247 - 251
Database
ACNP
SICI code
Abstract
H. Crapo raised in 1982 the following problem: If P is a complete lattice, is Retr (P) a complete lattice? here Retr (P) denotes the set of all retraction operators on P with the pointwise order, that is, f . g in Retr (P) iff f(x) . g(x) for every x in P. An affirmative answer will be given in the present paper.