CHAPTER VI - INFINITE-DIMENSIONAL SPACES

Abstract

This chapter discusses infinite-dimensional spaces. It presents notions that distinguish some types of infinite-dimensional spaces from general infinite-dimensional spaces. The chapter also presents a brief account of infinite dimensional spaces and especially of countable-dimensional spaces. It is a natural idea to extend definitions of Ind and ind by transfinite induction. The chapter further presents some results of the theory of finite-dimensional spaces to countable-dimensional spaces. One has not succeeded in finding an imbedding theorem for finite-dimensional general metric spaces that is very analogous to the one for the separable case.