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In a recent paper, Engle, Hanusch and Thiemann showed that there is a uniquestate on the reduced holonomy-flux $\ast$-algebra of homogeneous isotropic loopquantum cosmology, that is invariant under residual diffeomorphims. This resulthas been claimed to be true both for the Ashtekar-Bojowald-Lewandowskiframework and for that introduced by the present author. Unfortunately, theuniqueness proof relies on an incorrect argument which spoils the second case.In our short note, we are going to patch this issue, this way keeping the niceuniqueness result in both cases. Moreover, we will even extend the underlyingoperator algebraic statements as this might help later for studyinghigher-dimensional models.

Continuity of States on Non-Unital Differential Algebras in Loop Quantum Cosmology