Boundary of a torus or sphere?

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SUMMARY

The boundary of a torus is defined as a null set, while the boundary of a sphere is also a null set. This conclusion is based on the properties of manifolds, where both the torus and sphere are classified as 2-manifolds. The discussion emphasizes the importance of starting with definitions to clarify these concepts, particularly in the context of topology.

PREREQUISITES
  • Understanding of 2-manifolds in topology
  • Familiarity with the concepts of boundaries in geometric spaces
  • Knowledge of null sets and their implications in mathematical definitions
  • Basic principles of manifold theory
NEXT STEPS
  • Research the properties of 2-manifolds in topology
  • Study the concept of boundaries in various geometric contexts
  • Explore the implications of null sets in mathematical definitions
  • Learn about different types of manifolds and their classifications
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Students of topology, mathematicians, and educators looking to deepen their understanding of geometric boundaries and manifold theory.

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Homework Statement


What is the boundary of a torus?

What is the boundary of a sphere?






The Attempt at a Solution


Both 0?
 
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Neither of them is 0. In both cases it is a symbol that looks like 0 I suppose. Why don't you start with the defintions, since many things are clearly implied by them?
 
It is not the null set is it?

THe boundary must be a 1-manifold?
 

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