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**Handbook of the history of general topology. Volume 1.**
*(English)*
Zbl 0888.54001

History of Topology, 1. Dordrecht: Kluwer Academic Publishers. ix, 397 p. (1997).

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Show indexed articles as search result.
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This account of the history of general topology has grown out of the special session on this topic at the American Mathematical Society meeting in San Antonio, Texas, 1993.

Since the first chapter by M. Fréchet, “Généralisation d’un théorème de Weierstrass” [C. R. Acad. Sci., Paris 139, 848-850 (1904; JFM 35.0389.02)] and F. Hausdorff’s classic book, “Grundzüge der Mengenlehre” (1914; JFM 45.0123.01), there have been numerous developments in a multitude of directions and there have been many interactions with a great number of other mathematical fields. We have tried to cover as many of these as possible. Most contributions concern either individual topologists, specific schools, specific periods, specific topics or a combination of these.

In this first volume there are articles covering the work of F. Hausdorff, F. Riesz, H. Tietze, R. L. Moore, B. Knaster, W. Hurewicz, L. E. J. Brouwer, L. Vietoris, F. B. Jones. Furthermore there are articles covering ‘The beginning of topology in the United States’, ‘Topologists in the 1940’s’, ‘Topology in Japan’. And finally there are papers covering ‘Dimension theory’, ‘Continuum theory’, ‘Rings of continuous functions in the 1950s’, ‘Categorical topology’, ‘Sequential convergence spaces’, ‘Interactions between topology and functional analysis’.

Indexed articles:

Preuß, Gerhard, Felix Hausdorff (1868-1942), 1-19 [Zbl 0995.01534]

Thron, W. J., Frederic Riesz’ contributions to the foundations of general topology, 21-29 [Zbl 0899.54001]

Reitberger, Heinrich, The contributions of L. Vietoris and H. Tietze to the foundations of general topology, 31-40 [Zbl 0904.54001]

Fitzpatrick, Ben jun., Some aspects of the work and influence of R. L. Moore, 41-61 [Zbl 0899.54003]

Charatonik, Janusz J., The works of Bronisław Knaster (1893-1980) in continuum theory, 63-78 [Zbl 0899.54002]

Borsuk, Karol, Witold Hurewicz – life and work, 79-84 [Zbl 0898.54001]

Rudin, Mary Ellen, The early work of F. B. Jones, 85-96 [Zbl 0954.54001]

Jones, F. Burton, The beginning of topology in the United States and the Moore school, 97-103 [Zbl 0899.54004]

Stone, A. H., Some topologists of the 1940s, 105-109 [Zbl 0898.54002]

Miroslav Katětov (1918-1995), 111 [Zbl 0901.01016]

Katětov, Miroslav; Simon, Petr, Origins of dimension theory, 113-134 [Zbl 0902.54002]

Koetsier, Teun; van Mill, Jan, General topology, in particular dimension theory, in the Netherlands: The decisive influence of Brouwer’s intuitionism, 135-180 [Zbl 0904.01019]

Nagata, J., The flowering of general topology in Japan, 181-241 [Zbl 0935.54002]

Henriksen, Melvin, Rings of continuous functions in the 1950s, 243-253 [Zbl 0898.54003]

Herrlich, Horst; Strecker, George, Categorical topology – its origins, as exemplified by the unfolding of the theory of topological reflections and coreflections before 1971, 255-341 [Zbl 0906.54001]

Frič, R., History of sequential convergence spaces, 343-355 [Zbl 0902.54003]

Kreyszig, Erwin, Interaction between general topology and functional analysis, 357-389 [Zbl 0901.54001]