  For a given compact Hausdorff space $X$, we construct the space $OS_{f}(X)$
of normed, order-preserving, weakly additive, positively homogeneous and
semi-additive functionals (for brevity, semi-additive functionals) and it is
proved that the hyperspace $\exp\, X$ of the space $X$ is a deformation retract
of the constructed space. Further we show that the shapes of the spaces
$OS_{f}(X)$ and $\exp\, X$ coincide. We establish that if the space $\exp\, X$
is contractible, then the space $OS_{f}(X)$ is also contractible.
