Normalized General Relativity: Non-closed Universe and Zero Cosmological Constant

We discuss the cosmological constant problem, at the minisuperspace level, within the framework of the so-called normalized general relativity (NGR). We prove that the Universe cannot be closed, and reassure that the accompanying cosmological constant $\Lambda$ generically vanishes, at least classically. The theory does allow, however, for a special class of $\Lambda \not=0$ solutions which are associated with static closed Einstein universe and with Eddington-Lema\^{\i}tre universe.