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May 22nd, 2014, 12:22 AM  #1 
Senior Member Joined: Apr 2014 From: zagreb, croatia Posts: 234 Thanks: 33 Math Focus: philosophy/found of math, metamath, logic, set/category/order/number theory, algebra, topology  Universal Algebra
In the book A Course In Universal Algebra by Burris, chapter 3 Algebraic Lattices and Subuniverses, can someone help me with Theorem 3.2. If we are given an algebra $\displaystyle A$, then Sg is an algebraic closure operator on $\displaystyle A$. http://www.math.uwaterloo.ca/~snburr...lgebra2012.pdf 
May 27th, 2014, 08:16 PM  #2 
Senior Member Joined: Apr 2014 From: zagreb, croatia Posts: 234 Thanks: 33 Math Focus: philosophy/found of math, metamath, logic, set/category/order/number theory, algebra, topology 
Two lattices $L_1$ and $L_2$ are isomorphic iff there is a bijection $\alpha$ from $L_1$ to $L_2$ such that both $\alpha$ and $\alpha^{1}$ are orderpreserving. Can anyone please prove this? . 

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