Which topologies are same as the Euclidean Metric Topology in $R^n$?

Question

Are Standard Topology , Usual Topology , Product Topology, Euclidean Metric Topology , Square Metric Topology , $L^1$ Norm Metric Topology same in $R^n$ ?

I am little bit confused after reading some early chapters of Mukresh. I think they all are same. Can you please ensure me? Thank You.

Answer 1

Yes, they're all the same. If you want a different one, you can try the discrete topology, for instance.