This paper investigates the cosmological implications of $f(Q)$ gravity, a modified theory of gravity based on non-metricity, in non-flat geometries. The authors perform a detailed dynamical-system analysis, considering an arbitrary $f(Q)$ function. They find that the cosmological scenario admits a dark-matter dominated point and a dark-energy dominated de Sitter solution. However, the main contribution of the paper is the discovery of additional critical points that exist solely due to curvature. These include curvature-dominated accelerating points, which are unstable and can describe the inflationary epoch, and a point where both the dark-matter and dark-energy density parameters are between zero and one, potentially alleviating the coincidence problem. Additionally, there is a saddle point completely dominated by curvature. To illustrate these findings, the authors apply their analysis to the power-law case $f(Q) = \eta Q^n$, showing that the system exhibits a transition from an initial accelerated expansion stage to an intermediate matter-dominated non-accelerating era, and finally to a final accelerated expansion phase. The curvature density parameter exhibits a peak at intermediate times. These features, along with the potential alleviation of cosmological tensions, make $f(Q)$ gravity in non-flat geometries an interesting and promising area for further investigation.This paper investigates the cosmological implications of $f(Q)$ gravity, a modified theory of gravity based on non-metricity, in non-flat geometries. The authors perform a detailed dynamical-system analysis, considering an arbitrary $f(Q)$ function. They find that the cosmological scenario admits a dark-matter dominated point and a dark-energy dominated de Sitter solution. However, the main contribution of the paper is the discovery of additional critical points that exist solely due to curvature. These include curvature-dominated accelerating points, which are unstable and can describe the inflationary epoch, and a point where both the dark-matter and dark-energy density parameters are between zero and one, potentially alleviating the coincidence problem. Additionally, there is a saddle point completely dominated by curvature. To illustrate these findings, the authors apply their analysis to the power-law case $f(Q) = \eta Q^n$, showing that the system exhibits a transition from an initial accelerated expansion stage to an intermediate matter-dominated non-accelerating era, and finally to a final accelerated expansion phase. The curvature density parameter exhibits a peak at intermediate times. These features, along with the potential alleviation of cosmological tensions, make $f(Q)$ gravity in non-flat geometries an interesting and promising area for further investigation.