A proof of the basic measure extension theorem of Carathéodory (Q5945159)

The author gives a topological proof of the measure extension theorem of Carathéodory. As mentioned by the author, such a topological approach to measure extension theorems in a more general context was developed -- besides others -- by \textit{L. Drewnowski} [Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 20, 277-286 (1972; Zbl 0249.28005)], \textit{W. Herer} [Commentat. Math. 19, 73-80 (1976; Zbl 0354.28008)], \textit{D. Maharam} [Port. Math. 44, 265-282 (1987; Zbl 0636.28002)] and \textit{H. Weber} [Arch. Math. 27, 412-423 (1976; Zbl 0331.28005)].