$\overset{\circ}B$-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 $\overset{\circ}B $-connected set and a few classical structural characteristics of sets, in particular, we examine whether $\overset{\circ}B $-complete sets have connected or path-connected intersections with closed and open balls. A $\overset{\circ}B $-complete Chebyshev set in an asymmetric Efimov–Stechkin space is shown to be $B$-connected, i.e., it has connected intersections with closed balls. All problems under consideration are posed in asymmetric and classical normed spaces.