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}).