The MV-Algebraic Loomis–Sikorski Theorem
An MV-algebra A is said to be σ-complete if its underlying lattice is closed under countable suprema. It follows that A is semisimple, whence it is isomorphic to an MV-algebra A* of continuous [0,1]-valued functions defined on some compact Hausdorff space X.
KeywordsBoolean Algebra Compact Hausdorff Space Countable Sequence Nonempty Closed Subset Clopen Subset
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