Complete Sets: Approximative and Structural Properties

We address the approximative and structural properties of approximating sets in asymmetric spaces. More precisely, we study the interrelations between the new concept of -connected set and a few classical structural characteristics of sets, in particular, we examine whether -complete sets have connected or path-connected intersections with closed and open balls. A -complete Chebyshev set in an asymmetric Efimov–Stechkin space is shown to be -connected, i.e., it has connected intersections with closed balls. All problems under consideration are posed in asymmetric and classical normed spaces.