A most popular model in the family of two-dimensional uniformly-frustrated XY models is the antiferromagnetic model on a triangular lattice [AF XY(t) model]. Its ground state is both continuously and twofold discretely degenerated. Different phase transitions possible in such systems are investigated. Relevant topological excitations are analyzed and a new class of such (vortices with a fractional number of circulation quanta) is discovered. Their role in determining the properties of the system proves itself essential. The characteristics of phase transitions related to breaking of discrete and continuous symmetries change. The phase diagram of the "generalized" AF XY(t) model is constructed. The results obtained are rederived in the representation of the Coulomb gas with half-integer charges, equivalent to the AF XY(t) model with the Berezinskii-Villain interaction.