We shall discuss the partition regular properties of topological groups, and obtain an extension of Hindman’s theorem where the monochromatic sets of finite sums are required to satisfy additional topological constraints. In particular, our results imply that for every nowhere dense subset $C\subseteq \mathbb R^n$ there exists an open set $P\supseteq C$ such that for every finite coloring of $\mathbb Q^n\setminus P$ there exists a family $\mathcal A$ of sequences in $\mathbb Q^n\setminus P$ satisfying the following conditions: (i) the set of finite sums $\operatorname{FS}(A)$ is a closed discrete subset of $\mathbb R^n$ for all $A\in\mathcal A$; (ii) the set $\bigcup_{A\in\mathcal A}\operatorname{FS}(A)$ is monochromatic; and (iii) the set $\bigcup_{A\in\mathcal A}\operatorname{FS}(A)$ is dense in an open unbounded subset of $\mathbb R^n$. The aforementioned result was obtained using a new characterization of spaces whose Stone-Čech compactifications possess remote points.