Is $\mathbb{Q}^\omega$ a homogeneous space?
This space is defined as a set of all rational sequences, also sometimes denoted $\mathbb{Q}^\mathbb{N}$. It is the set of all functions from the naturals to the rationals. I assume the standard product topology on $\mathbb{Q}^\omega$
I am asking about homogeneity of this space, since it would mean there is a "rich" group of automorphisms here. Which would tell that a lot of points are "topologically the same".
My guess would be that $\mathbb{Q}^\omega$ is homogeneous, since $\mathbb{Q}$ is homogeneous too, but I dont have any idea how to prove it.
Thank you for your thoughts.