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Let   ${\mathcal B}$   be an infinite subset of   $\{1,2,\dots\}$  . We characterize arithmetic and dynamical properties of the   ${\mathcal B}$  -free set   ${\mathcal F}_{\mathcal B}$   through group theoretical, topological and measure theoretic properties of a set   $W$   (called the  window ) associated with   ${\mathcal B}$  . This point of view stems from the interpretation of the set   ${\mathcal F}_{\mathcal B}$   as a weak model set. Our main results are:   ${\mathcal B}$   is taut if and only if the window is Haar regular; the dynamical system associated to   ${\mathcal F}_{\mathcal B}$   is a Toeplitz system if and only if the window is topologically regular; the dynamical system associated to   ${\mathcal F}_{\mathcal B}$   is proximal if and only if the window has empty interior; and the dynamical system associated to   ${\mathcal F}_{\mathcal B}$   has the “naïvely expected” maximal equicontinuous factor if and only if the interior of the window is aperiodic.

Dynamics of $\boldsymbol{{\mathcal B}}$ -Free Sets: A View Through the Window