  Let $(U, R)$ be an approximation space with $U$ being non-empty set and $R$
being an equivalence relation on $U$, and let $\overline{G}$ and
$\underline{G}$ be the upper approximation and the lower approximation of
subset $G$ of $U$. A topological rough group $G$ is a rough group
$G=(\underline{G}, \overline{G})$ endowed with a topology, which is induced
from the upper approximation space $\overline{G}$, such that the product
mapping $f: G\times G\rightarrow \overline{G}$ and the inverse mapping are
continuous. In the class of topological rough groups, the relations of some
separation axioms are obtained, some basic properties of the neighborhoods of
the rough identity element and topological rough subgroups are investigated. In
particular, some examples of topological rough groups are provided to clarify
some facts about topological rough groups. Moreover, the version of open
mapping theorem in the class of topological rough group is obtained. Further,
some interesting open questions are posed.
