By Krzysztof Maurin
The terribly fast advances made in arithmetic because international battle II have led to research changing into a huge organism unfold ing in all instructions. long gone for reliable absolutely are the times of the good French "courses of research" which embodied the full of the "ana lytical" wisdom of the days in 3 volumes-as the classical paintings of Camille Jordan. might be for this reason present-day textbooks of anal ysis are disproportionately modest relative to the current state-of-the-art. extra: they've got "retreated" to the nation ahead of Jordan and Goursat. in recent times the scene has been altering speedily: Jean Dieudon ne is supplying us his monumentel components d'Analyse (10 volumes) written within the spirit of the nice French path d'Analyse. To the easiest of my wisdom, the current publication is the single one among its dimension: ranging from scratch-from rational numbers, to be precise-it is going directly to the idea of distributions, direct integrals, research on com plex manifolds, Kahler manifolds, the idea of sheaves and vector bun dles, and so forth. My target has been to teach the younger reader the sweetness and wealth of the unsual global of contemporary mathematical research and to teach that it has its roots within the nice arithmetic of the nineteenth century and mathematical physics. i know that the younger brain eagerly beverages in appealing and tough issues, rejoicing within the indisputable fact that the realm is excellent and teeming with experience.