Polygonal-path approximations on the path spaces of quantum-mechanical systems

Properties of the subset of polygonal paths in the Hilbert space of paths referring to ad-dimensional quantum-mechanical system are examined. The results are used to discuss various types of polygonal-path approximations appearing in the functional-integration theory. The uniform approximation is applied to extend the definition of the Feynman maps from our previous paper and to prove consistency of this extension. Relations of the extendedF _−i map to the Wiener integral are given.