Grundzüge der Mengenlehre
| Author | Felix Hausdorff |
|---|---|
| Translator | John R. Aumann et al. (English translation) |
| Country | Germany |
| Language | German |
| Subject | Set theory, mathematics |
| Genre | Non-fiction |
Publication date | April 1914 |
Published in English | 1957 (English translation) |
Grundzüge der Mengenlehre (German for "Basics of Set Theory") is a book on set theory written by Felix Hausdorff.
First published in April 1914, Grundzüge der Mengenlehre was the first comprehensive introduction to set theory. Besides the systematic treatment of known results in set theory, the book also contains chapters on measure theory and topology, which were then still considered parts of set theory. Hausdorff presented and developed original material which was later to become the basis for those areas. In 1927 Hausdorff published an extensively revised second edition under the title Mengenlehre (German for "Set Theory"), with many of the topics of the first edition omitted. In 1935 there was a third German edition, which in 1957 was translated by John R. Aumann et al. into English under the title Set Theory.
Chelsea Publishing Company reprinted the German 1914 edition in New York City in German in 1944, 1949, 1965, 1978 and 1991 but never issued an English translation of this first edition (or the 1927 second edition) to date. When the American Mathematical Society took over and set up AMS Chelsea Publishing it published editions in 2005 and 2021.
References
- Blumberg, Henry (1920), "Hausdorff's Grundzüge der Mengenlehre", Bulletin of the American Mathematical Society 27 (3): 116–129, doi:10.1090/S0002-9904-1920-03378-1.
- Gehman, H. M. (1927), "Hausdorff's Revised Mengenlehre", Bull. Amer. Math. Soc. 33 (6): 778–781, doi:10.1090/S0002-9904-1927-04478-0
- Hausdorff, Felix (1914), Grundzüge der Mengenlehre, Leipzig: Veit, ISBN 978-0-8284-0061-9, https://archive.org/details/grundzgedermen00hausuoft Reprinted by Chelsea Publishing Company in 1944, 1949 and 1965 [1].
- Hausdorff, F. (1935) [1927], Mengenlehre (3 ed.), Berlin-Leipzig: de Gruyter Republished by Dover Publications, New York, N. Y., 1944
- Hausdorff, Felix (1962) [1957], Set theory (2 ed.), New York: Chelsea Publishing Company, ISBN 978-0821838358 Republished by AMS-Chelsea 2005.
- Scholz, Erhard (2005), Felix Hausdorff and the Hausdorff edition, http://www2.math.uni-wuppertal.de/~scholz/preprints/ENLbioHaus.pdf. Extended edition of a chapter in The Princeton Companion to Mathematics.
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