locally convex topological vector space
Definition Let be a topological vector space over a subfield
of the complex numbers
(usually taken to be or ). If the topology of has a basis where each member isa convex set, then is a locally convex topologicalvector space [1].
Though most vector spaces occurring in practice are locally convex, the spaces for are examples of spaces which are not locally convex.
References
- 1 G.B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd ed, John Wiley & Sons, Inc., 1999.