TITLE: What does "topological dual of a Banach space" mean?
QUESTION [5 upvotes]: I am not sure what does the "topological" imply. Thanks.

REPLY [8 votes]: The topological dual is defined as the space of all bounded linear functionals on your space. It is called this to differentiate it from the algebraic dual, which includes all linear functionals, including the non-bounded ones.