A weakly Lindelöf space which does not have the property $^*\mathcal{U}_{fin}(\mathcal{O},\mathcal{O})$

Servet Soyarslan, Süleyman Önal

Published 2022-12-07Version 1

We show that there exists a Tychono? weakly Lindel\"of space which does not have the property $^*\mathcal{U}_{fin}(\mathcal{O},\mathcal{O})$. This result answers the following open questions. [2] Does a weakly Lindel\"of space have the property $^*\mathcal{U}_{1}(\mathcal{O},\mathcal{O})$? [3] Is there a Tychono? 1-star-Lindel\"of space which does not have the property $^*\mathcal{U}_{fin}(\mathcal{O},\mathcal{O})$?