  We investigate the possibility of spatially homogeneous and inhomogeneous
chiral fermion-antifermion condensation and superconducting fermion-fermion
pairing in the (1+1)-dimensional model by Chodos {\it et al.} [ Phys. Rev. D
61, 045011 (2000)] generalized to continuous chiral invariance. The
consideration is performed at nonzero values of temperature $T$, electric
charge chemical potential $\mu$ and chiral charge chemical potential $\mu_5$.
It is shown that at $G_1<G_2$, where $G_1$ and $G_2$ are the coupling constants
in the fermion-antifermion and fermion-fermion channels, the
$(\mu,\mu_5)$-phase structure of the model is in a one-to-one correspondence
with the phase structure at $G_1>G_2$ (called duality correspondence). Under
the duality transformation the (inhomogeneous) chiral symmetry breaking (CSB)
phase is mapped into the (inhomogeneous) superconducting (SC) phase and vice
versa. If $G_1=G_2$, then the phase structure of the model is self-dual.
Nevertheless, the degeneracy between the CSB and SC phases is possible in this
case only when there is a spatial inhomogeneity of condensates.
