Talk:Lindelöf space

Examples?
It would be cool if this article provided some examples of spaces that are and aren't Lindelöf. -76.22.99.215 06:10, 25 September 2007 (UTC)

Products of Lindelöf Spaces
The following set of sets is presented as a cover for Sorgenfrey plane S

1. The set of all points (x, y) with x < y

2. The set of all points (x, y) with x + 1 > y

3. For each real x, the half-open rectangle [x, x + 2) × [−x, −x + 2)

But the two first set already cover all plane. In fact, for any point (x,y), either x -y

3. For each real x, the half-open rectangle [x, x + 2) × [−x, −x + 2)

Then, the rest of the text is OK. —Preceding unsigned comment added by 189.25.30.180 (talk) 02:31, 30 January 2010 (UTC)

Hereditarily Lindelöf versus strongly Lindelöf
A search of the literature (google, mathse, mathoverflow, dan ma's topology blog, Willard, Engelking, etc) shows that the terminology hereditarily Lindelöf is much more common than strongly Lindelöf, both in the context of general topology and in the context of measure theory (see Bogachev's book for example). Furthermore, hereditarily Lindelöf has unambiguous meaning, whereas strongly Lindelöf is sometimes used with a different meaning altogether (see https://www.semanticscholar.org/paper/A-NOTE-ON-STRONGLY-LINDELO%CC%88F-SPACES-Ganster/04b50b66a69e898fb5fec820765244f07d9beddc for example). For these reasons, I will flip the role of the two terms and make hereditarily Lindelöf the main accepted terminology. PatrickR2 (talk) 21:50, 3 October 2020 (UTC)