Natural generalization of the class of ℒ∞-spaces in the category of b-spaces

A new class of b-spaces, called ε b-spaces, is defined. This class is a natural generalization of the class of ℒ_∞-spaces. Some properties of ε b-spaces are established. __________ Translated from Problemy Matematicheskogo Analiza, No. 33, 2006, pp. 3–11.