  We construct two Frechet algebras admitting countably many mutually
inequivalent Frechet algebra topologies. The second example is a modification
of the maiden (and first) example of a non-Banach Frechet algebra with two
inequivalent Frechet algebra topologies, considered by Read to show that the
famous Singer-Wermer conjecture does not hold in the Frechet case. However the
conjecture does hold by the second example which also admits countably many
mutually equivalent Frechet algebra topologies.
