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

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