Autor:

Bečvářová, I. Netuka:

Jarník's notes of the lecture course Punktmengen und reelle Funktionen by P. S. Aleksandrov  (Göttingen 1928),

Prague, 2010, 143 pages,

TABLE OF CONTENTS

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Pavel Sergeevich Aleksandrov (1896–1982) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

Vojtěch Jarník (1897–1970) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Mathematics in G¨ottingen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Jarník’s Notebooks from G¨ottingen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Aleksandrov’s Punktmengen und reelle Funktionen . . . . . . . . . . . . . . . . . . . . . . . .51

Summary of Results and Bibliographical and Historical Comments . . . . . . . .91

Table of Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113

Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Index of Names . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

ABSTRACT

This publication is devoted to unique archival materials – Jarník’s mathematical

notebook, which he wrote during his studies at the University in

G¨ottingen in the academic year 1927/1928 and which contains a record of

the lecture course he attended given by Pavel Sergeevich Aleksandrov titled

Punktmengen and reelle Funktionen [Point sets and real functions].

The first chapter of the present text gives a short description of Aleksandrov’s

life and scientific as well as pedagogical activities. His lecturing in

G¨ottingen and collaboration with German mathematicians are the main topics

of that chapter.

The second chapter is devoted to Jarník’s life and work and mainly to

his studies at G¨ottingen in the academic years 1923/1924, 1924/1925 and

1927/1928.

The third chapter briefly deals with the founding of the University in G¨ottingen

and the development of mathematical studies and research there. The

productive and inspiring atmosphere in the G¨ottingen mathematical center in

the 1920’s and 1930’s is brought to life with the help of long passages chosen

from the recollections of some outstanding mathematicians who lectured or

studied there.

The fourth chapter provides a general account of Jarník’s fourteen notebooks

and a short description of his fifth notebook which contains Aleksandrov’s

lectures Punktmengen and reelle Funktionen.

The sixth and the seventh chapters are the heart of this publication. Firstly,

Aleksandrov’s lectures are rewritten from Jarník’s manuscript and then detailed

mathematical, historical and bibliographical comments follow.

Illustrations and copies from Jarník’s notebook and some archival materials

and documents can be found at the end of the book, followed by an index of

names.

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