Approximative and structural properties of sets in asymmetric spaces

Structural and approximative properties of sets implying their solarity are studied. It is shown that, in any finite-dimensional polyhedral space, each strict sun admits a continuous $\varepsilon$-selection for all $\varepsilon>0$ and the metric projection onto it has cell-like values. In general asymmetric spaces, sufficient conditions for solarity of Chebyshev sets are put forward.