What is the English translation for Einsatzunghomöomorphismus in German?

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SUMMARY

The term "Einsatzunghomöomorphismus" is a misinterpretation of the correct term "Einsetzunghomöomorphismus," which translates to "evaluation homomorphism" in English. This concept refers to a mapping where elements from one space, such as the polynomial ring \(\mathbb{R}[\xi]\), are evaluated by substituting complex numbers into the indeterminate. The discussion highlights the importance of precise terminology in mathematical contexts, as minor errors can lead to significant confusion in research.

PREREQUISITES
  • Understanding of homeomorphism in topology
  • Familiarity with polynomial rings, specifically \(\mathbb{R}[\xi]\)
  • Knowledge of complex numbers and their properties
  • Basic grasp of homomorphism concepts in algebra
NEXT STEPS
  • Research "evaluation homomorphism" in algebraic structures
  • Study the properties of homeomorphisms in topology
  • Explore the applications of polynomial rings in complex analysis
  • Learn about the relationship between algebra and topology in mathematics
USEFUL FOR

Mathematicians, students of algebra and topology, and anyone interested in the precise language of mathematical concepts will benefit from this discussion.

trambolin
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Can anyone identify the word something like

"Einsatzunghomöomorphismus",

and give me the english translation?

It is the homeomorphism where you evaluate the elements by plugging elements from another space. Well, that is not a good sentence...

Suppose you consider the polynomial ring [itex]\mathbb{R}[\xi][/itex] and you start taking elements from that space and plugging complex numbers into the indeterminate to create a mapping [itex]\mathbb{C}[/itex] to most probably [itex]\mathbb{C}[/itex] or a subspace of it.

Hmm... this is not good also but I hope you get the idea, sorry for the sloppiness but I am actually looking for it to study.
 
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trambolin said:
Can anyone identify the word something like

"Einsatzunghomöomorphismus",

I've hever heard (or read) that word. Do you mean "Einsetzunghomöomorphismus" or ""Auswertungshomöomorphismus"..? Where did you come across this word?

What about this:
http://planetmath.org/encyclopedia/EvaluationHomomorphism.html
 
Last edited by a moderator:
Damn, all those letters and I miss only one of them, that made my search completely useless. Nevertheless, thank you very much for the fast response...
 

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