  In this note we establish the weak unique continuation theorem for caloric
functions on compact $RCD(K,2)$ spaces and show that there exists an $RCD(K,4)$
space on which there exist non-trivial eigenfunctions of the Laplacian and
non-stationary solutions of the heat equation which vanish up to infinite order
at one point. We also establish frequency estimates for eigenfunctions and
caloric functions on the metric horn. In particular, this gives a strong unique
continuation type result on the metric horn for harmonic functions with a high
rate of decay at the horn tip, where it is known that the standard strong
unique continuation property fails.
