Remarks on star-Lindelöf spaces.(English)Zbl 1006.54032

Summary: We prove the following statements: (1) Every linked-Lindelöf Tikhonov space can be embedded in a star-Lindelöf Tikhonov space as a closed $$G_\delta$$-subspace. (2) There exists a star-Lindelöf (hence, a $$1 \frac 12$$-star-Lindelöf) Tikhonov space having a zero-set which is not $$1\frac 12$$-star-Lindelöf. The statement (1) gives an answer to [M. Bonanzinga and M. V. Matveev, East-West J. Math. 2, No. 2, 171-179 (2000; Zbl 0997.54035), Question 3] and to [M. V. Matveev, A survey on star-covering properties, Topological Atlas Preprint No. 330 (1998), Question 46] and (2) answers negatively a question that M. V. Matveev stated in the lastly cited preprint.

MSC:

 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) 54B10 Product spaces in general topology 54D55 Sequential spaces