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 is a convex set, then is a locally convex topological vector space .
Though most vector spaces occurring in practice are locally convex, the spaces for are examples of spaces which are not locally convex.
- 1 G.B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd ed, John Wiley & Sons, Inc., 1999.
|Title||locally convex topological vector space|
|Date of creation||2013-03-22 13:44:03|
|Last modified on||2013-03-22 13:44:03|
|Last modified by||mathcam (2727)|