Rational Witt spaces were introduced by Deninger in 2018. I will recall their definition and explain how the points of these spaces, in nice cases, can be described in terms of multiplicative ring maps. Over Z_p we will modify the space of such points valued in a rank one valuation ring V by imposing a continuity condition, inverting Frobenius formally, and completing. We will then explain how parts of these spaces can be interpreted in terms of untilts of V^{\flat}, or using the language of diamonds.