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

In summary, the conversation is discussing the possibility of a bounded space without a boundary, which would require embedding it in a higher spatial dimension. The definitions of bounded, boundary, and embedding are also mentioned, but are not explicitly defined. However, the conversation ends with the suggestion to ask this question in a forum dedicated to General Relativity.
  • #1
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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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  • #2
Define bounded space, define boundary, define embedding.
 
  • #3
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
 
  • #4
Sorry, but this is much too vague to give a mathematical answer. Perhaps you should ask this in the GR forum.
 

1. What is a bounded space without a boundary without embedding?

A bounded space without a boundary without embedding is a mathematical concept in topology and geometry. It refers to a space that has a finite size or volume, but does not have a physical or geometric boundary, and cannot be embedded or placed in a higher-dimensional space.

2. Is it possible for such a space to exist in the real world?

No, a bounded space without a boundary without embedding is a purely theoretical concept. In the physical world, all spaces have some sort of boundary or edge, and can be embedded in a higher-dimensional space.

3. What implications does this concept have in mathematics or physics?

This concept has implications in various fields, including topology, geometry, and theoretical physics. It challenges our understanding of space and its properties, and has led to new discoveries and theories in these areas.

4. How is this concept related to infinity?

Bounded spaces without a boundary without embedding are often used to study the concept of infinity. They can help us understand the properties and limitations of infinite spaces, and how they can be represented or visualized.

5. Are there any real-world examples or applications of this concept?

While this concept may not have direct real-world applications, it has been used in theoretical physics to study the properties of black holes and the behavior of matter in extreme conditions. It also has applications in computer graphics and animation, where it is used to create and manipulate virtual spaces.

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