Existence of (n-k)D objects in an nD world

Question

Is it possible for an object to be completely (n-k)-dimensional in an n-dimensional world?

Dimensions here refer to spatial dimensions.

For example, can a purely 2D object exist in a 3D world?

Answer 1

This is not really a question about mathematics, and also it’s not entirely clear what you’re asking. Any object made of atoms will contain protons and electrons whose probability distribution is nonzero at all points in an n-dimensional neighborhood.

In practice at the macroscale one can assume objects are codimensional (that hair is a curve, or paper a surface) and this approximation is good enough for many purposes.

Answer 2

At least for some mathematical objects that can be considered to rationalise the intuitive intuitive concept of dimension, the answer is "yes". For example, a $n $-dimensional vector space over any field contains subspaces of all dimensions $0,1,...,n $.