/sci/ - Science & Math

Is the space of real sequences [math] \mathbb{R}^{\omega}[/math] equiped witht the (Tychonoff) product topology a countable union of compact sets? Is it Lindelöf? I assume the former implies the latter. I find this particuler topology hard to work with, can't construct an open covering that could provde a counterexample the open sets are rather counterintuitive and feel unfamiliar,