Q:

Question on n-manifolds

It seems to be more of a conceptual problem than anything, but I was wondering, if a manifold $M$ can be locally parametrized (homeomorphic) by a coordinate chart $F:(u_1,....,u_n) \rightarrow p \in M$, can the manifold have dimension greater than $n$? Also why is it that the manifold has dimension $n?$ 
I would appreciate some clear clarification. 

A:

The dimension is the dimension of the space in which the local parametrization is defined, and the dimension cannot be greater. 
See here: https://en.wikipedia.org/wiki/Invariance_of_domain

