复分析

...what a remarkabe property it is of *two*-dimensional space that it is possible to interpret points *within it* as the fundamental Euclidean transformations *acting on it*.

在球面表示中，对于加法和乘法没有简单的解释，其方便在于无穷远点不再特殊

事实上，只有解析函数或全纯函数可以自由地进行微分和积分。它们是法文“Théorie des fonctions”或德文“Funktionentheorie"意义下唯一真正的”函数"。

A continuous function on a compact set Ω is bounded and attains a maximum and minimum on Ω

Similarly, a closed set F is connected if one cannot write F = F1 ∪ F2 where F1 and F2 are disjoint non-empty closed sets.

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