The older name for topology was "analysis situs", analysis of place. Why that was changed is unknown to me, but the topo- root is just Greek for place and it would be a stretch to assume anything else without good evidence. A French mathematician named, IIRC, Jean Pont wrote a book called, "L'Histoire de la topologie algébrique avant Poincaré" that traces topology, at least algebraic topologie to Euler's solution to the bridges of Königsberg problem. I think V-F+E = 2 came next. Michael On Fri, 2 Jul 2010, Eduardo J. Dubuc wrote:
Grothendieck introduced the term "topos" simply out of "topology" and "topological space".
we should wonder who and why introduced "topology" and "topological space".
Dusko Pavlovic wrote:
It might be fair to remember that "Topoi" is the title of 6th book or Aristotle's Organon. "On Categories" is the title of the 1st book of Organon. Both concepts were very actively used by scolastic philosophers. Maybe we are their heirs of some sort ;)
It would be interesting to know about the motivations of people who introduced these terms into mathematics. I think that MacLane said at one point that there was a terminological link through Rudolf Carnap, thus through neokantians. The notion of categories plays a prominent role in Kant's first Critique. But it is even more interesting if the term topos was introduced with an intentional reference to *dialectics*, which is what that part of Organon is about.
-- dusko
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Yes, this is Grothendieck's stated intention, in the article "Topos" written with Verdier in SGA 4 (p. 301). But at the same time he and his friends knew well that topo, with plural topos, is ordinary French for a little speech, and is common slang for a school essay. This comes from the long-time use of "topos" as a term in rhetoric taken from Aristotle. I have not found older uses of the specific term "humility topos," but "topos" in this rhetorical sense is not postmodern. It is one of the oldest scholarly terms. Colin 2010/7/2 Steve Vickers <s.j.vickers@cs.bham.ac.uk>:
I've assumed (and told people) that "topos" was a back-formation from "topology" - that Grothendieck's intention was to imply that toposes were the structures of which topology was truly the study. (The argument falls into two parts: (a) to carry out topology you need sheaves and not just opens, and (b) there are suitable categories of sheaves that don't arise from ordinary spaces.)
Certainly it is my own intention to stress the "generalized topological space" nature of toposes; but is my assumption about Grothendieck's intention actually correct?
Steve.
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Yes, according to Pont, the name "topologie" comes from Johann Benedikt Listing, a student of Gauss, who introduced it for the first time in 1836. He referred to analysis situs and geometry but decided that a new name was required and suggested "topology". Best, Jean-Pierre Le 10-07-02 à 11:41, Michael Barr a écrit :
The older name for topology was "analysis situs", analysis of place. Why that was changed is unknown to me, but the topo- root is just Greek for place and it would be a stretch to assume anything else without good evidence.
A French mathematician named, IIRC, Jean Pont wrote a book called, "L'Histoire de la topologie algébrique avant Poincaré" that traces topology, at least algebraic topologie to Euler's solution to the bridges of Königsberg problem. I think V-F+E = 2 came next.
Michael
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participants (3)
-
Colin McLarty -
Jean-Pierre Marquis -
Michael Barr