The development of function spaces with particular reference to their origins in integral equation theory

Bernkopf, Michael

doi:10.1007/bf00412288

Cited by 46 publications

(8 citation statements)

References 19 publications

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“…41 A transcription of this letter (Riesz 1907b) is included in Appendix B and (Rodríguez 2006). On the development of function spaces, see Bernkopf (1966). Apparently, Bernkopf did not know of this letter from Riesz.…”

Section: Letters From Hungarymentioning

confidence: 92%

Frigyes Riesz and the emergence of general topology

Rodríguez

2014

Arch. Hist. Exact Sci.

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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.

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Section: Letters From Hungarymentioning

confidence: 92%

Frigyes Riesz and the emergence of general topology

Rodríguez

2014

Arch. Hist. Exact Sci.

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“…You have just passed your PhD exam." 5 In our opinion, this is the source of the urban legend about Banach's doctorate. We will never know whether Nikodym gave Turowicz a twisted account of his own PhD exam, changing the main protagonist's name in the process, or whether Turowicz missed something.…”

Section: Banach's Doctorate: a Case Of Mistaken Identitymentioning

confidence: 96%

“…His dissertation was published two years later as [2]. For an excellent analysis of the results contained therein, see [5,15,18,23]. Banach's dissertation was of fundamental importance for the development of mathematics in the twentieth century, which, however, was not evident at the outset.…”

Section: Banach's Doctorate: a Case Of Mistaken Identitymentioning

confidence: 99%

Banach’s Doctorate: A Case of Mistaken Identity

Ciesielska

Ciesielski

2021

Math Intelligencer

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On the occasion of the hundredth anniversary of that famous talk, a bench with the figures of Banach and Nikodym (designed by Stefan Dousa) was unveiled in the Planty Garden in Krakó w (see [7]). The following year, a picture of this bench appeared on the cover of this magazine (Mathematical Intelligencer 39:1). 2 Since we mentioned the cover of the Mathematical Intelligencer featuring the bench with Banach and Nikodym, we might mention as well that the cover of the Mathematical Intelligencer 17:1 (1975) exhibits a poster with Sierpiń ski's face formed by his space-filling curve, designed by Fritz Lott.

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“…The subject of integral equations continues as an important area of study in applied mathematics; and for an introduction that includes a review of much recent literature, see Kress [149]. For an interesting historical account of the development of functional analysis as it was affected by the development of the theory of integral equations, see Bernkopf [36]. From hereon, to simplify notation, for a scalar λ and an operator K : V → V , we use λ − K for the operator λI − K, where I : V → V is the identity operator.…”

Section: The Fredholm Alternative Theoremmentioning

confidence: 99%