I have some questions regarding point set topologies. I know if one is given a topology, you can extract the base for a topology, also, if given two identical bases, they can generate the same topology.
but are the following possible
If I am given two identical bases $B_1=B_2$, can $B_1$ generate a topology different from $B_2$. Likewise, if given two non identical bases, is it true sometimes that the two different bases
My other question are the same as the above but for the case of subbase.
Thank you in advance. Seth