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单词 LocallyConvexTopologicalVectorSpace
释义

locally convex topological vector space


Definition Let V be a topological vector spaceMathworldPlanetmath over a subfieldMathworldPlanetmath of the complex numbersMathworldPlanetmathPlanetmath (usually taken to be or ). If the topology of Vhas a basis where each member isa convex set, then V is a locally convex topologicalvector space [1].

Though most vector spaces occurring in practice are locally convex, the spaces Lp for 0<p<1 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.
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