On cardinality bounds for \(\theta^n\)-Urysohn spaces
- 13 Downloads
We introduce the class of \(\theta^n\)-Urysohn spaces and the \(n\)-\(\theta\)-closure operator. \(\theta^n\)-Urysohn spaces generalize the notion of a Urysohn space and we consider their relationship with S(n)-spaces, studied in ,  and . We estabilish bounds on the cardinality of these spaces and cardinality bounds if the space is additionally homogeneous.
Key words and phrasesUrysohn homogeneous space \(\theta\)-closure \(\theta^n\)-closure Lindelöf degree
Mathematics Subject Classification54A25 54D10
Unable to display preview. Download preview PDF.
The authors are very grateful to the anonymous reviewer for valuable comments and suggestions to improve the quality of the paper and for suggesting Question 1. The first author would like to thank also Professor I. Gotchev for good conversations relating \(\theta^n\)-Urysohn spaces and S(n)-spaces.
- 7.F. Cammaroto and Lj. Kočinac, On \(\theta \)-tightness, Facta Universitatis (Niš), Ser. Math. Inform., 8 (1993), 77–85Google Scholar
- 10.R. Engelking, General Topology, Heldermann Verlag (1989)Google Scholar
- 13.A. Osipov, On the cardinality of \(S(n)\)-spaces, arXiv:1809.09587
- 17.N. V. Veličko, H-closed topological spaces, Mat. Sb. (N.S.), 70 (112) (1966), 98–112 (in Russian)Google Scholar