The order bidual of C( X ) for a realcompact space

1AbstractIt is well known that the bidual of C(X) for a compact space X, supplied with the Arens product, is isometrically isomorphic as a Banach algebra to for some compact space . The space is unique up to homeomorphism. We establish a similar result for realcompact spaces: The order bidual of C(X) for a realcompact space X, when supplied with the Arens product, is isomorphic as an f-algebra to for some realcompact space . The space is unique up to homeomorphism.Mathematics Subject Classification (2020): Primary: 46E05Secondary: 46A4046M40Key words: Vector latticescontinuous functionsbidualsdirect limitsinverse limits