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When Is the Space of Continuous Functions a Hyperarchimedian MV-Algebra?
Francis Jordan and Homeira Pajoohesh

In this article we consider ๐ถ(๐‘‹,[0,1]) as an MV-algebra. We show that ๐ถ(๐‘‹, [0, 1]) is hyperarchimedian if and only if ๐‘‹ is a finite union of spaces that only admit constant real-valued continuous functions. We also characterize the essential ideals and implicative ideals of ๐ถ(๐‘‹, [0, 1]). Lastly, we characterize the molecules of ๐ถ(๐‘‹, [0, 1]).

Keywords: MV-algebra, completely regular space, hyperarchimedian MV-algebra

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