Metric spaces: 100 years

[anhinga_anhinga]

I only knew Fréchet as a mathematician, who came up with the notion of derivative in normed vector spaces, which made sense to me. It turnes out that he is behind a number of fundamental definitions we are using today.

Maurice Fréchet introduced metric spaces in his work Sur quelques points du calcul fonctionnel, Rendic. Circ. Mat. Palermo 22(1906) 1-74.

The term compact was introduced by Fréchet in 1906.

Biography: Maurice René Fréchet

Comments

[anhinga-anhinga.livejournal.com]

from the bio: "Fréchet wrote an outstanding doctoral dissertation Sur quelques points du calcul fonctionnel submitted on 2 April 1906. In it he introduced the concept of a metric space, although he did not invent the name 'metric space' which is due to Hausdorff. The thesis concerns 'functional operations' and 'functional calculus' and is developed from ideas due to Hadamard and Volterra. The importance of the thesis is that it develops axiomatic analysis systems providing an abstraction of different objects studied by analysis in a similar way to group theory providing an abstraction of algebraic systems. This parallel is drawn by Fréchet himself who requires sufficient structure on his abstract systems so that limits and continuity can be studied. He defines a functional operation as a numerically valued function defined on arbitrary objects which he wants to include points, lines, functions, numbers, surfaces etc. The functional calculus of his thesis is then the systematic study of functional operations."

[misha-b.livejournal.com]

Did not know that. Impressive.

[anhinga-anhinga.livejournal.com]

Yes, it seems that he is very underappreciated.

And especially, in his own country: "Although widely honoured, it does appear that Fréchet was more highly rated outside France than inside it. He was invited to address the International Congress of Mathematicians in Bologna in 1928 and in Oslo in 1932. He was elected to the Polish Academy of Sciences in 1929 and the Royal Society of Edinburgh in 1947. He was also a member of the International Institute of Statistics. He lost out many times in elections to the Academy of Sciences, eventually being elected in 1956 when he was 78 years old.

[faceless-lady.livejournal.com]

The term compact was introduced by Fréchet in 1906.

угу?? 8->

[anhinga-anhinga.livejournal.com]

у? ;-)

видишь, оказалось, что он не только придумал понятие производной в правильной степени общности, которая позволяет разобраться во всей этой путанице между производными и дифференциалами и, вообще, даёт правильную интуицию, но, оказывается, и сделал ещё несколько вполне фундаментальных вещей, которыми мы всё время пользуемся.. хороший диссер человек написал :-)))

[faceless-lady.livejournal.com]

позволяет разобраться во всей этой путанице между производными и дифференциалами

пожалуй, я всё ещё путаюсь.. :-) (в правильной степени общности)..по крайней мере, я не знала, что между ними была прежде путаница ;-)

[(Anonymous)]

в моей голове точно была :-) но я думаю, что почти у всех есть :-)

вот, например, задают в конце первого семестра по анализу такой дурацкий вопрос -- что такое "второй дифференциал"? что скажешь? :-)

[(Anonymous)]

скажу, что лектор невнятно это объяснил...;-) оно и правда, так, честно говоря, и было...впрочем, могу глянуть в шпаргалку. ;-)

[(Anonymous)]

глянь :-)))