subracting dimensions

[Pjpic]

Can there be a place(?) where only 5 dimesional object are allowed? Or would there always be the need for a 4 dimensional surface of the 5 dimensional obect?


If you'll always need to be able to subtract a dimension (the edge of a 2d plane is a 1d line and the end of a 1d line is a 0d point), would the surface of the zero dimensional "point" have a dimension of -1?

[zhentil]

Why does it need to have a "surface"? What's the surface of the sphere?

The boundary of a manifold can be empty, but if it exists, it has dimension one less. A zero-dimensional manifold can't have boundary, for obvious reasons.

[slider142]

Can there be a place(?) where only 5 dimesional object are allowed? Or would there always be the need for a 4 dimensional surface of the 5 dimensional obect?


If you'll always need to be able to subtract a dimension (the edge of a 2d plane is a 1d line and the end of a 1d line is a 0d point), would the surface of the zero dimensional "point" have a dimension of -1?

What is your definition of dimension? Ie., how are you able to determine that the object is 5 dimensional and not 4 dimensional or 6 dimensional?
If the object is a 5 dimensional topological manifold, then locally one can construct a 5-dimensional vector space; it is then trivial that there is a 4-dimensional subspace.

[Pjpic]

What is your definition of dimension? Ie., how are you able to determine that the object is 5 dimensional and not 4 dimensional or 6 dimensional?
If the object is a 5 dimensional topological manifold, then locally one can construct a 5-dimensional vector space; it is then trivial that there is a 4-dimensional subspace.

I don't know how the number of dimensions is determined. Do all objects of x dimesional topological manifold have a (x-1) subspace? Would this be true for x =1? For x = 0?