A space of pseudoquotients $mathcal{B}(X,S)$ is defined as equivalence classes of pairs $(x,f)$, where $x$ is an element of a non-empty set $X$, $f$ is an element of $S$, a commutative semigroup of injective maps from $X$ to $X$, and $(x,f) sim (y,g)
$ if $gx=fy$. In this note we consider a generalization of this construction where the assumption of commutativity of $S$ by Ore type conditions. As in the commutative case, $X$ can be identified with a subset of $mathcal{B}(X,S)$ and $S$ can be extended to a group $G$ of bijections on $mathcal{B}(X,S)$. We introduce a natural topology on $mathcal{B}(X,S)$ and show that all elements of $G$ are homeomorphisms on $mathcal{B}(X,S)$.
