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It is well-known that there are four distinct basic types (two Big Bangtypes, Lemaitre and Big Crunch type) for solutions of the general Friedmannequation with positive cosmological constant, where radiation and matter do notcouple (see e.g. [2, p.7]. In that paper the system of case distinctionparameters contains a "critical radiation parameter" $\sigma_{cr}$. The presentnote contains the constructive description of the so-called {\em border lines}between Big Bang/Big Crunch type and Big Bang/Lemaitre type for so-calledHubble solutions of the Friedmann equation by two smooth function branches,expressing the cosmological constant as unique functions of the matter andradiation density (which is considered as a parameter). These functions satisfysimple asymptotic relations w.r.t. the matter density. They are constructed asthe solutions of the equation $\sigma=\sigma_{cr}.

On the border lines between the regions of distinct solution type for solutions of the Friedmann equation satisfying the Hubble condition