The paper discusses the evolution of the Fermi surface (FS) topology in electron-doped cuprates near optimal doping, using a one-band Hubbard Hamiltonian. The FS topology undergoes two significant changes: the first at optimal doping, where an additional hole pocket appears at the nodal point, and the second in the overdoped regime ($\sim 18\%$), where antiferromagnetism disappears and a large $(\pi, \pi)$-centered metallic FS forms. These transitions are supported by Hall effect and penetration depth experiments on $Pr_{2-x}Ce_xCuO_{4-\delta}$ (PCCO) and spectroscopic measurements on $Nd_{2-x}Ce_xCuO_{4-\delta}$ (NCCO). The authors also explore how these topological transitions manifest in the superconducting properties, particularly in the $T-$dependence of the penetration depth $\lambda$, which reflects the interplay between antiferromagnetic order and superconductivity. The study provides insights into the pairing symmetry and the coexistence of electron- and hole-like quasiparticles, which could lead to non-Fermi-liquid behavior and Bose-Einstein condensation.The paper discusses the evolution of the Fermi surface (FS) topology in electron-doped cuprates near optimal doping, using a one-band Hubbard Hamiltonian. The FS topology undergoes two significant changes: the first at optimal doping, where an additional hole pocket appears at the nodal point, and the second in the overdoped regime ($\sim 18\%$), where antiferromagnetism disappears and a large $(\pi, \pi)$-centered metallic FS forms. These transitions are supported by Hall effect and penetration depth experiments on $Pr_{2-x}Ce_xCuO_{4-\delta}$ (PCCO) and spectroscopic measurements on $Nd_{2-x}Ce_xCuO_{4-\delta}$ (NCCO). The authors also explore how these topological transitions manifest in the superconducting properties, particularly in the $T-$dependence of the penetration depth $\lambda$, which reflects the interplay between antiferromagnetic order and superconductivity. The study provides insights into the pairing symmetry and the coexistence of electron- and hole-like quasiparticles, which could lead to non-Fermi-liquid behavior and Bose-Einstein condensation.