  The structure of the joint phase diagram demonstrating high-$T_c$
superconductivity of copper oxides is studied on the basis of the theory of
interaction-induced flat bands. Prerequisites of an associated topological
rearrangement of the Landau state are established, and related non-Fermi-liquid
(NFL) behavior of the normal states of cuprates is investigated. We focus on
manifestations of this behavior in the electrical resistivity $\rho(T)$,
especially the observed gradual crossover from normal-state $T$-linear behavior
$\rho(T,x)=A_1(x)T$ at doping $x$ below the critical value $x_c^h$ for
termination of superconductivity, to $T$-quadratic behavior at $x>x_c^h$, which
is incompatible with predictions of the conventional quantum-critical-point
scenario. It is demonstrated that at $x<x^h_c$, in agreement with available
experimental data, the coefficient $A_1( x)$ is decomposed into the product of
two factors, one of which changes linearly with doping $x$, while the second is
universal, being of the Planckian form.
