Undergrad Can there be a bounded space w/o a boundary w/o embedding?

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SUMMARY

The discussion centers on the concept of bounded space and its relationship with boundaries and embeddings in higher spatial dimensions. A bounded space is defined as having a finite size, while a boundary is characterized as having an edge or point distinct from the rest of the space. Embedding refers to the process of curving a surface of x spatial dimensions within an area of x+1 spatial dimensions. The conversation highlights the complexity of these definitions and suggests that further clarification may be needed in a specialized forum, such as one focused on General Relativity (GR).

PREREQUISITES
  • Understanding of basic topology concepts
  • Familiarity with spatial dimensions and their properties
  • Knowledge of General Relativity principles
  • Ability to define and differentiate between bounded spaces, boundaries, and embeddings
NEXT STEPS
  • Research the definitions and properties of bounded spaces in topology
  • Explore the concept of boundaries in mathematical contexts
  • Study embeddings in higher-dimensional spaces, particularly in relation to General Relativity
  • Engage with discussions in specialized forums focused on General Relativity for deeper insights
USEFUL FOR

This discussion is beneficial for mathematicians, physicists, and students of theoretical physics who are exploring the concepts of space, boundaries, and dimensionality in their studies.

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Can there be a bounded space without a boundary without embedding in a higher spatial dimension?

This seems to be the kind of question I get stuck on when the big bang comes up.

Thanks
 
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Define bounded space, define boundary, define embedding.
 
I wouldn't say my definitions are correct but:
bounded = of a finite size --
boundary = having an edge or point different from the rest--
embedding = curving a surface of x spatial dimensions using and area of x+1 spatial dimensions
 
Sorry, but this is much too vague to give a mathematical answer. Perhaps you should ask this in the GR forum.
 

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