On a generalization of Σ-spaces

Abstract

In order to simultaneously generalize the class of M-spaces and (7-spaces, K. Nagami introduced ^-spaces. Subsequently, E. Michael defined a class of ^-spaces. In this paper we will discuss the class of 2^-spaces which lies between ^-spaces and ^-spaces and which contains all images of I'-spaces under closed continuous maps. 1* Introduction* Recently K. Nagami [6] has investigated a new class of spaces, called I'-spaces, containing two different classes of generalized metric spaces; i.e. the class of M-spaces (cf. [4]) as well as the class of -spaces (cf. [5], [7]).