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

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Discussion Overview

The discussion revolves around the concept of a bounded space without a boundary and the implications of embedding in higher spatial dimensions. It touches on theoretical aspects related to cosmology and geometry.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions whether a bounded space can exist without a boundary and without embedding in a higher dimension.
  • Another participant requests definitions for "bounded space," "boundary," and "embedding" to clarify the discussion.
  • A third participant offers tentative definitions, suggesting that "bounded" refers to finite size, "boundary" indicates an edge or distinct point, and "embedding" involves curving a surface in higher dimensions.
  • One participant expresses that the original question is too vague for a mathematical answer and suggests moving the discussion to a more specialized forum.

Areas of Agreement / Disagreement

There is no consensus on the definitions or the feasibility of the concepts discussed. Multiple competing views and uncertainties remain regarding the nature of bounded spaces and boundaries.

Contextual Notes

The discussion lacks precise definitions and may depend on varying interpretations of key terms. The mathematical implications of the concepts are not fully explored.

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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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