quasi
Posts:
11,483
Registered:
7/15/05


Re: Homomorphism of posets and lattices
Posted:
Sep 18, 2013 5:52 AM


If X,Y are posets, a function f:X > Y is called an order homomorphism if x <= y implies f(x) <= f(y).
If X,Y are posets, a bijective function f:X > Y is called an order isomorphism if both f and f^(1) are order homomorphisms.
Posets X,Y are said to be order isomorphic if there exists an order isomorphism f:X > Y.
Questions:
Let X,Y be posets and suppose f:X > Y and g:Y > X are order homomorphisms.
(1) If f,g are both injective, must X,Y be order isomorphic?
(2) If f,g are both surjective, must X,Y be order isomorphic?
quasi

