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May 22nd, 2014, 12:22 AM   #1
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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
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May 27th, 2014, 08:16 PM   #2
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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 order-preserving.

Can anyone please prove this?
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