Constant function: Difference between revisions

Revision as of 12:44, 5 May 2020

Revision as of 11:32, 11 July 2020

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==Other properties==

For functions between [[preorder|preordered sets]], constant functions are both [[order-preserving]] and [[order-reversing]]; conversely, if ''f'' is both

order-preserving and order-reversing, and if the [[Domain of a function|___domain]] of ''f'' is a [[lattice (order)|lattice]], then ''f'' must be constant.

* Every constant function whose [[Domain of a function|___domain]] and [[codomain]] are the same set X is a [[left zero]] of the [[full transformation monoid]] on X, which implies that it is also [[idempotent]].