  Given a scheme $X$ over $\mathbb{Z}$ and a hyperfield $H$ which is equipped
with topology, we endow the set $X(H)$ of $H$-rational points with a natural
topology. We then prove that; (1) when $H$ is the Krasner hyperfield, $X(H)$ is
homeomorphic to the underlying space of $X$, (2) when $H$ is the tropical
hyperfield and $X$ is of finite type over a complete non-Archimedean valued
field $k$, $X(H)$ is homeomorphic to the underlying space of the Berkovich
analytificaiton $X^{\textrm{an}}$ of $X$, and (3) when $H$ is the hyperfield of
signs, $X(H)$ is homeomorphic to the underlying space of the real scheme $X_r$
associated with $X$.
