We make the following three observations regarding a question popularized by Katznelson: is every subset of \({\mathbb {Z}}\) which is a set of Bohr recurrence also a set of topological recurrence? (i) If G is a countable abelian group and \(E\subseteq G\) is an \(I_0\) set, then every subset of \(E-E\) which is a set of Bohr recurrence is also a set of topological recurrence. In particular every subset of \(\{2^n-2^m : n,m\in {\mathbb {N}}\}\) which is a set of Bohr recurrence is a set of topological recurrence. (ii) Let \({\mathbb {Z}}^{\omega }\) be the direct sum of countably many copies of \({\mathbb {Z}}\) with standard basis E. If every subset of \((E-E)-(E-E)\) which is a set of Bohr recurrence is also a set of topological recurrence, then every subset of every countable abelian group which is a set of Bohr recurrence is also a set of topological recurrence. (iii) Fix a prime p and let \({\mathbb {F}}_p^\omega \) be the direct sum of countably many copies of \({\mathbb {Z}}/p{\mathbb {Z}}\) with basis \(({\mathbf {e}}_i)_{i\in {\mathbb {N}}}\). If for every p-uniform hypergraph with vertex set \({\mathbb {N}}\) and edge set \({\mathcal {F}}\) having infinite chromatic number, the Cayley graph on \(\mathbb F_p^\omega \) determined by \(\{\sum _{i\in F}{\mathbf {e}}_i:F\in {\mathcal {F}}\}\) has infinite chromatic number, then every subset of \(\mathbb F_p^\omega \) which is a set of Bohr recurrence is a set of topological recurrence.