compact map; compact $R_\delta$-set
The aim of this note is
1. to show that some results (concerning the structure of the solution set of equations (18) and (21)) obtained by Czarnowski and Pruszko in  can be proved in a rather different way making use of a simle generalization of a theorem proved by Vidossich in ; and
2. to use a slight modification of the "main theorem" of Aronszajn from  applying methods analogous to the above mentioned idea of Vidossich to prove the fact that the solution set of the equation (24), (25) (studied in the paper ) is a compact $R_\delta$.
 E. F. Beckenbach, R. Bellman: Inequalities
. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. MR 0158038
| Zbl 0186.09606
 K. Czarnowski, T. Pruszko: On the structure of fixed point sets of compact maps in $B_0$ spaces with applications to integral and differential equations in unbounded domain
. J. Math. Anal. Appl. 154 (1991), 151-163. DOI 10.1016/0022-247X(91)90077-D
| MR 1087965
 V. Šeda, Z. Kubáček: On the set of fixed points of a compact operator. Czech. Math. J., to appear.