  Following several papers in the prior literature, we study the relationship
between order bounded operators, topologically bounded operators and
topologically continuous operators. Our main contribution is two folded: (i) we
provide a set of counterexamples to illustrate several extant results in the
literature; (ii) we give conditions for the space of order bounded operators to
coincide with the space of topologically bounded operators as well as
conditions for these two spaces to coincide with the space of topologically
continuous operators.
