  Ricci solitons on Finsler spaces, previously developed by the present
authors, are a generalization of Einstein spaces, which can be considered as a
solution to the Ricci flow on compact Finsler manifolds. In the present work it
is shown that on a Finslerian space, a forward complete shrinking Ricci soliton
is compact if and only if it is bounded. Moreover, it is proved that a compact
shrinking Finslerian Ricci soliton has finite fundamental group and hence the
first de Rham cohomology group vanishes.
