Predictions of the top-pair production cross section in electron-proton (ep) collisions at the future circular collider hadron-electron (FCC-he) and the large hadron electron collider (LHeC) in the leading order (LO) and the next-to-leading order (NLO) approximations in perturbative quantum chromodynamics (QCD) are presented. Numerical results for the top structure functions and the ratio of structure functions are computed at the renormalization scale μ2=Q2+4mt2 in the collinear generalized double asymptotic scaling (DAS) approach. These results are presented in terms of the effective parameters of the parameterization of F2(x,Q2), where relying on a Froissart-bounded. These quantitative results can be important for future collider experiments at the center-of-mass energy frontier and the improvement of the phenomenological models for the development of the cosmic ray cascades in ultra-high-energy domain. We obtained the uncertainties because of the power-law behavior x−Δ of the collinear parton distribution functions (PDFs), the factorization, and renormalization scales, on the top properties at high inelasticity for the FCC-he center-of-mass (CM) energy at the NLO approximation.