Erratum: TOPoS: VI. The metal-weak tail of the metallicity distribution functions of the Milky Way and the Gaia -Sausage-Enceladus structure (Astronomy and Astrophysics (2021) 651 (A79) DOI: 10.1051/0004-6361/202140816)

We realised that there was a mistake in the code that computed parameters for the photometric data sample. The effective temperature was not computed according to the formula in footnote 3. As a consequence the surface gravity and metallicity were also computed incorrectly. We also realised that almost 50% of the lines in the table were duplicated. Furthermore, for 301 763 stars, the interpolation arrived at the edge in metallicity of the synthetic grid (+0.5) and the program was not extrapolating. We removed these stars from the final catalogue. A new catalogue, containing 12 894 443 unique stars, has been produced correcting these two mistakes and deposited at CDS. In the paper this impacts only Fig. 8, which is corrected in this corrigendum, and the number of stars in this catalogue cited in Sect. 5.2; it should read: "The final sample, which we refer to in the following as 'photometric', consists of 12 894 443 unique stars". None of the conclusions of the paper are altered by this change. (Figure Presented).