**Abstract:** We introduce a weakening of the Generalized Continuum Hypothesis, which we will refer to as the *Prevalent Singular cardinals Hypothesis* (PSH), and show it implies that every topological space of density and weight $\aleph_{\omega_1}$ is not hereditarily Lindelöf.

The assumption PSH is very weak, and in fact holds in all currently known models of ZFC.

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**Citation information:**

A. Rinot, *On topological spaces of singular density and minimal weight*, Topology Appl., 155(3): 135-140, 2007.