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Abstract Recent work has shown that near-infrared (NIR) Hubble Space Telescope (HST) photometry allows us to disentangle multiple populations (MPs) among M dwarfs of globular clusters (GCs) and to investigate this phenomenon in very-low-mass (VLM) stars. Here, we present the color–magnitude diagrams of nine GCs and the open cluster NGC 6791 in the F110W and F160W bands of HST, showing that the main sequences (MSs) below the knee are either broadened or split, thus providing evidence of MPs among VLM stars. In contrast, the MS of NGC 6791 is consistent with a single population. The color distribution of M dwarfs dramatically changes between different GCs, and the color width correlates with the cluster mass. We conclude that the MP ubiquity, variety, and dependence on GC mass are properties common to VLM and more-massive stars. We combined UV, optical, and NIR observations of NGC 2808 and NGC 6121 (M4) to identify MPs along with a wide range of stellar masses (∼0.2–0.8  ⊙ ), from the MS turnoff to the VLM regime, and measured, for the first time, their mass functions (MFs). We find that the fraction of MPs does not depend on the stellar mass and that their MFs have similar slopes. These findings indicate that the properties of MPs do not depend on stellar mass. In a scenario where the second generations formed in higher-density environments than the first generations, the possibility that the MPs formed with the same initial MF would suggest that it does not depend on the environment. 

ABSTRACT In the fourth paper of this series, we present – and publicly release – the state-of-the-art catalogue and atlases for the two remaining parallel fields observed with the Hubble Space Telescope for the large programme on ω Centauri. These two fields are located at ∼12 arcmin from the centre of the globular cluster (in the west and south-west directions) and were imaged in filters from the ultraviolet to the infrared. Both fields were observed at two epochs separated by about 2 yr that were used to derive proper motions and to compute membership probabilities.