SPACES

Abstract. In this paper, we shall classify small weakly infinite-dimensional spaces and consider the compactifications and the completions of the spaces. 1. Introduction. All spaces in this paper are assumed to be normal T1. By a completion of a metrizable space X we mean here a completely metrizable space X which contains a dense subspace homeomorphic to X. Our terminology and notations follow lB1] and [E]. P. Borst, in [B1], introduced the concept of small weak infinite dimensionality, and showed the followin