The main purpose of this article is to give a new method and new results on a very old topic: the comparison of the Riemann processes of summation (R, κ) with other summation processes. The motivation comes from the study of continuous unimodular functions on the circle, their Fourier series and their winding numbers. My oral presentation in Poznań at the JM-100 conference exposed the ways by which this study was developed since the fundamental work of Brézis and Nirenberg on the topological

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... ree [5] . I shall shorten the historical part in the present article; it can be found in [3], [8] and [9]. 2010 Mathematics Subject Classification: Primary 42A16, 40G99, 26A16.