By Gerhard Preuß (auth.), C. E. Aull, R. Lowen (eds.)

This e-book is the 1st one in all a piece in numerous volumes, treating the historical past of the improvement of topology.
The paintings comprises papers which are labeled into four major components. therefore there are contributions facing the existence and paintings of person topologists, with particular colleges of topology, with examine in topology in a variety of nations, and with the improvement of topology in numerous sessions. The paintings isn't limited to topology within the strictest experience but in addition offers with purposes and generalisations in a vast experience. hence it additionally treats, e.g., express topology, interactions with useful research, convergence areas, and uniform areas. Written through experts within the box, it incorporates a wealth of knowledge which isn't on hand anyplace else.

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5. Arcs and pseudo-arcs An early characterization of the arc as a nondegenerate compact continuum with no more than two non-separating points is due to Moore. He also, in a joint paper [34] with 1. R. Kline, gave necessary and sufficient conditions for a closed planar set to be a subset of a planar arc. Incidentally, to the best of my knowledge this is the only joint paper either of them ever wrote. As was the case with most of Moore's research results, this theorem appeared in Foundations. That Foundations is still a useful research tool is attested to by A.

Ann. 87 (1922),150--151. [20] _ _ , Beitrage zur allgemeinen Topologie: I. Axiome fUr verschiedene Fassungen des Umgebungsbegriffs, Math. Ann. 88 (1923),290--312. II. Uber die EinfUhrung uneigentlicher Elemente, Math. Ann. 91 (1924),210--224. III. Uber die Komponenten offener Mengen, Monatsh. f Math. u. Phys. 32 (1924), 15-17. , Beziehungen zwischen den verschiedenen Zweigen der Topologie, Encyklopiidie der Math. Wiss. 13. Teubner, Leipzig, 1914-1931, 144-237. , Uber die Metrisation der kompakten topologischen Raume, Math.

MOORE R. L. Moore 1969, Annette Calhoun 53 54 BEN FITZPATRICK JR. 8. Teaching; the Moore method A book on the' history of general topology which omitted a discussion of R. L. Moore would be like a history of American popular music which failed to mention Irving Berlin, and an article on R. L. s melodies and not mentioning his lyrics; the two are inseparable. The previous sentence sets the tone for this section; much of what follows is the author's opinion. I believe, however, that many mathematicians who have been influenced by Moore share, in varying degrees, the opinions put forward.

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