ИСТИНА

We prove that a~closed set~$M$ with lower semi-continuous metric projection in a Banach space of dimension $n\le 3$. is a~sun, has intersections with closed ball, and admits a~continuous selection of the metric projection. Besides, it is shown that a~closed set with lower semi-continuous metric projection in a finite-dimensional space is a~sun, is $\mathring B $-infinitely connected, is $\mathring B$-contractible, is a~$\mathring B$-retract and admits a~continuous $\varepsilon$-selection for any $\varepsilon>0$.