Acta Mathematica Hungarica

, Volume 159, Issue 1, pp 109–123 | Cite as

On cardinality bounds for \(\theta^n\)-Urysohn spaces

  • F. A. BasileEmail author
  • N. Carlson
  • J. Porter


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 [9], [14] and [18]. We estabilish bounds on the cardinality of these spaces and cardinality bounds if the space is additionally homogeneous.

Key words and phrases

Urysohn homogeneous space \(\theta\)-closure \(\theta^n\)-closure Lindelöf degree 

Mathematics Subject Classification

54A25 54D10 


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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.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science, Physics and Earth SciencesUniversity of MessinaMessinaItaly
  2. 2.Department of MathematicsCalifornia Lutheran University, Thousand OaksCaliforniaUSA
  3. 3.Department of MathematicsUniversity of KansasLawrenceUSA

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