A point-free approach to the Nakaoka spectrum of a Tambara functor

For $G$ a finite group and $T$ a $G$-Tambara functor, we construct the frame ${}_G(T)$ of radical Tambara ideals and show that its points are the Nakaoka primes. We show that this frame is spatial and coherent, and deduce that the Nakaoka spectrum is a spectral space, recovering a recent result of Chan and Spitz.