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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

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Discreteness of $D^{-1}D$ given that $D$ is uniformly discrete

Let $G$ be a topological group with unit element $e$. We say that $D\subseteq G$ is discrete if for all $x\in D$ there is a unit-neighborhood $U\subseteq G$ such that $x^{-1}D\cap U=\{e\}$. We say tha …