Cosmological parameters for a restricted class of closed big-bang universes

The half-plane defined by the deceleration parameter q and the density parameter sigma is reexamined to locate the regions appropriate to a closed big-bang universe which cannot expand without limit. Algebraic and numerical inequalities, relevant to these regions, are established for the cosmological constant, the radius of curvature of the 3-space, and the age of the universe. It is found that the permitted values of the various parameters lie within reasonably narrow limits.