Every infinite Hausdorff space has a countably infinite discrete subspace.
Now I know $R$ under usual topology has $Z$ and under "lower limit topology" also has $Z$ as such. So goes on for $R^{n}$ as long as $n$ is finite it will be $Z^{n}$ .But what about general Hausdorff Spaces? Please some hints.
I need to know what such discrete subspaces might look like for $R^{inf}$ since $Z^{\inf}$ or $N^{\inf}$ are not countable.
