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Without the successful work of Professor Kakutani on representing a unit vector space as a dense vector sub-lattice of , ⋅ C X , but V does not contain constant functions. This implies that we do need some different version of "Stone-Weierstrass theorem" so that we will be able to understand the "Stone-Weierstrass theorem" clearly and apply it to more places where they need this wonderful theorem.doi:10.4236/apm.2016.613071 fatcat:bfveuq2s5rgnre5wpu66ecf4xq