  In this paper, we obtain exact phantom (A)dS black hole solutions in the
context of $F(R)$ gravity with topological spacetime in four dimensions. Then,
we study the effects of different parameters on the event horizon. In the
following, we calculate the conserved and thermodynamic quantities of the
system and check the first law of thermodynamics for these kinds of black
holes. Next, we evaluate the local stability of the topological phantom (A)dS
black holes in $F(R)$ gravity by studying the heat capacity and the
geometrothemodynamic, where we show that the two approaches agrees. We extend
our study and investigate global stability by employing the Gibbs potential and
the Helmholtz free energy. In addition, the effects of different parameters on
local and global stabilities will be highlighted.
