(2) wi is not Lindelöf, and thus not second countable, because the intervals [0, a) for a
Posted: Thu May 12, 2022 6:52 am
- 2 Wi Is Not Lindelof And Thus Not Second Countable Because The Intervals 0 A For A Wi Are An Open Cover With No 1 (12.57 KiB) Viewed 40 times
Can someone expand on this proof? Omega_1 is the first
uncountable set of ordinals. Here, we are showing that omega_1 is
not Lindelof.
(2) wi is not Lindelöf, and thus not second countable, because the intervals [0, a) for a <wi are an open cover with no countable subcover.
Posted: Thu May 12, 2022 6:52 am
- 2 Wi Is Not Lindelof And Thus Not Second Countable Because The Intervals 0 A For A Wi Are An Open Cover With No 1 (12.57 KiB) Viewed 40 times
uncountable set of ordinals. Here, we are showing that omega_1 is
not Lindelof.
(2) wi is not Lindelöf, and thus not second countable, because the intervals [0, a) for a <wi are an open cover with no countable subcover.