caa a22 4500 606223940 CHVBK 20210128101141.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s00407-014-0144-6 doi (NATIONALLICENCE)springer-10.1007/s00407-014-0144-6 Rodríguez Laura University of Applied Sciences Fulda, Marquardstr. 35, 36039, Fulda, Germany aut Frigyes Riesz and the emergence of general topology [Elektronische Daten] The roots of ‘topological space' in geometry [Laura Rodríguez] In 1906, Frigyes Riesz introduced a preliminary version of the notion of a topological space. He called it a mathematical continuum. This development can be traced back to the end of 1904 when, genuinely interested in taking up Hilbert's foundations of geometry from 1902, Riesz aimed to extend Hilbert's notion of a two-dimensional manifold to the three-dimensional case. Starting with the plane as an abstract point-set, Hilbert had postulated the existence of a system of neighbourhoods, thereby introducing the notion of an accumulation point for the point-sets of the plane. Inspired by Hilbert's technical approach, as well as by recent developments in analysis and point-set topology in France, Riesz defined the concept of a mathematical continuum as an abstract set provided with a notion of an accumulation point. In addition, he developed further elementary concepts in abstract point-set topology. Taking an abstract topological approach, he formulated a concept of three-dimensional continuous space that resembles the modern concept of a three-dimensional topological manifold. In 1908, Riesz presented his concept of mathematical continuum at the International Congress of Mathematicians in Rome. His lecture immediately won the attention of people interested in carrying on his research. They promoted his ideas, thus assuring their gradual reception by several future founders of general topology. In this way, Riesz's work contributed significantly to the emergence of this discipline. Springer-Verlag Berlin Heidelberg, 2014 Archive for History of Exact Sciences Springer Berlin Heidelberg 69/1(2015-01-01), 55-102 0003-9519 69:1<55 2015 69 407 https://doi.org/10.1007/s00407-014-0144-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00407-014-0144-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rodríguez Laura University of Applied Sciences Fulda, Marquardstr. 35, 36039, Fulda, Germany aut NATIONALLICENCE 773 0- Archive for History of Exact Sciences Springer Berlin Heidelberg 69/1(2015-01-01), 55-102 0003-9519 69:1<55 2015 69 407