Antivarieties of unars

A complete description of the lattice of all antivarieties of unars is given. It is stated that there exist continuum many antivarieties of unars not having an independent basis of identities and a necessary and sufficient condition is specified under which a finite unar has an independent or finite basis of antiidentities. In addition, it is proved that the lattice of all antivarieties of unars is isomorphic to a lattice of $\mathcal A_{1,1}$-antivarieties, where $\mathcal A_{1,1}$ is a variety of unary algebras of a signature $\langle f,g\rangle$ defined by identities $f(g(x))=g(f(x))=x$.