Meaning of the word topological

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SUMMARY

The term "topological" refers to transformations that are continuous, ensuring that objects before and after the transformation remain 'topologically' equivalent. This concept is crucial in understanding topological actions, which can be either continuous or discontinuous. Notable contributions to this field include the work of Ed Witten in topological quantum field theory. For further exploration, resources such as Wikipedia articles on topology and group actions provide foundational knowledge.

PREREQUISITES
  • Understanding of continuous transformations in mathematics
  • Familiarity with topological equivalence
  • Basic knowledge of group actions
  • Awareness of topological quantum field theory concepts
NEXT STEPS
  • Research continuous and discontinuous transformations in topology
  • Study the concept of topological equivalence in detail
  • Explore group actions and their implications in mathematics
  • Investigate Ed Witten's contributions to topological quantum field theory
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This discussion is beneficial for mathematicians, physicists, and students interested in topology, group theory, and quantum field theory.

jinbaw
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when we say "a topological action", do we only mean that the action is metric free? or is there some other meaning for this expression? What does the word topological mean exactly? Thanks!
 
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It usually means that the given transformation is a continuous one so that the object before the transformation and the object after the transformation are 'topologically' equivalent. If you familiar with the concept of topological equivalent, it may be helpful.
 

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