  Generally-unbounded infinitesimal generators are studied in the context of
operator topology. Beginning with the definition of seminorm, the concept of
locally convex topological vector space is introduced as well as the concept of
Fr{\'e}chet space. These are the basic concepts for defining an operator
topology. Consequently, by associating the topological concepts with the
convergence of sequence, a suitable mathematical framework for obtaining the
logarithmic representation of infinitesimal generators is presented.
