  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.
