When Is the Space of Continuous Functions a Hyperarchimedian MV-Algebra?
Francis Jordan and Homeira Pajoohesh
In this article we consider 𝐶(𝑋,[0,1]) as an MV-algebra. We show that 𝐶(𝑋, [0, 1]) is hyperarchimedian if and only if 𝑋 is a finite union of spaces that only admit constant real-valued continuous functions. We also characterize the essential ideals and implicative ideals of 𝐶(𝑋, [0, 1]). Lastly, we characterize the molecules of 𝐶(𝑋, [0, 1]).
Keywords: MV-algebra, completely regular space, hyperarchimedian MV-algebra