We study the locally convex cones which have finite dimension. We introduce
the Euclidean convex quasiuniform structure on a finite dimensional cone. In
special case of finite dimensional locally convex topological vector spaces,
the symmetric topology induced by the Euclidean convex quasiuniform
structure reduces to the known concept of Euclidean topology. We prove that
the dual of a finite dimensional cone endowed with the Euclidean convex
quasiuniform structure is identical with it?s algebraic dual.