Question about some terminology

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Discussion Overview

The discussion revolves around the terminology used in topology, specifically the term "quotient topology" and its relation to "identification topology." Participants also inquire about the origins of certain mathematical terms like "ring," "ideal," and "soul." The scope includes conceptual clarification and exploratory reasoning regarding mathematical terminology.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions why "identification topology" is referred to as "quotient topology," suggesting that it aligns more with subtraction than division.
  • Another participant argues that the term "quotient" is analogous to "quotient groups," although they acknowledge that the notation could influence interpretation.
  • A participant expresses curiosity about the relationship between quotient topology and product topology, asking whether it involves inversion or other connections.
  • There is a request for anecdotes or explanations regarding the terminology of terms like "ring," "ideal," and "soul," indicating interest in the historical context of these terms.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of the term "quotient" in relation to identification topology, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

Participants have not fully explored the implications of their definitions or assumptions regarding the terms discussed, leaving some aspects of the terminology and its applications unclear.

Who May Find This Useful

This discussion may be of interest to those studying topology, mathematical terminology, or the historical context of mathematical concepts.

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Why the mathematician call identification topology "quotient topology"?from my viewpoint,identification topology bear an analogy with difference(minus),not quotient(divide)...BTW,Could anybody tell me the reason why the mathematicians who coined the term "ring","ideal","soul" called them like that,is there any anecdote about this terminology...tell me sth about them...Thx...
 
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I'm afraid I don't see what your problem is with "quotient". It is, of course, in analogy to "quotient groups". If the groups happened to be written in "additive notation", i.e. a+ b rather than ab, identity= 0 rather than 1, the quotient group might correspond to a "subtrahend group" but that it just cosmetic.

As for the other terms, yo might find this websit interesting:
http://members.aol.com/jeff570/mathword.html
 
Thanks for your reply.Well,what I doubt will be stated in the following.From the viewpoint of intuition,identification is a gluing operation.As an example,we could get cylinder from rectangle via identification IxI/~(where (0,y)~(1,y)),and we may see that the operation is like to subtract the edge ((0,y) or (1,y)) from the rectangle,so identification should have an analogy with subtraction,rather than division.and when we call it quotient topology,what is the relation between quotient topology and product topology?inversion or other?...
 

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