Some concepts of {\it operations on a subspace-topology}
are presented on a subspace of a given topological
space (Definitions~\ref{d200}, \ref{d210})
and some operation-open sets on the subspace are introduced (Definition~\ref{d300}).
And we investigate some relationships
among families of such operation-open sets (Theorem~\ref{t372}, Corollary~\ref{t380}).
As an application, we have an operation-closure formula for a subspace
(cf.\ Theorem~\ref{t389}).