# Article

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Keywords:
cardinal function; $\omega$H-set
Summary:
A subset $A$ of a Hausdorff space $X$ is called an $\omega$H-set in $X$ if for every open family $\Cal U$ in $X$ such that $A \subset \bigcup \Cal U$ there exists a countable subfamily $\Cal V$ of $\Cal U$ such that $A \subset \bigcup \{ \overline{V} : V \in \Cal V \}$. In this paper we introduce a new cardinal function $t_{s\theta}$ and show that $|A| \leq 2^{t_{s\theta}(X)\psi_{c}(X)}$ for every $\omega$H-set $A$ of a Hausdorff space $X$.
References:
[1] Bella A.: A couple of questions concerning cardinal invariants. Q & A in General Topology 14.2 (1996), pages ???. MR 1403339 | Zbl 0856.54002
[2] Bella A., Cammaroto F.: On the cardinality of Urysohn spaces. Canad. Math. Bull. 31 (1988), 153-158. MR 0942065 | Zbl 0646.54005
[3] Bella A., Yaschenko I.V.: Embeddings into first countable spaces with H-closed like properties. preprint. MR 1601642 | Zbl 0939.54003
[4] Bella A., Porter J.: Local cardinal functions of H-closed spaces. Comment. Math. Univ. Carolinae 37.2 (1996), 371-374. MR 1399007 | Zbl 0854.54003
[5] Dow A.: An introduction to applications of elementary submodels in topology. Topology Proceedings 13 (1988), 17-72. MR 1031969
[6] Dow A.: More set-theory for topologists. Topology Appl. 64 (1995), 243-300. MR 1342520 | Zbl 0837.54001
[7] Dow A., Porter J.: Cardinalities of H-closed spaces. Topology Proceedings 7 (1982), 27-50. MR 0696618 | Zbl 0569.54004
[8] Engelking R.: General Topology. Sigma Series in Pure Mathematics 6, Heldermann Verlag, Berlin (1989). MR 1039321 | Zbl 0684.54001
[9] Fedeli A., Watson S.: Elementary submodels and cardinal functions. Topology Proceedings 20 (1995), 91-110. MR 1429175 | Zbl 0894.54008
[10] Hodel R.E.: Cardinal functions I. 1-61 Handbook of Set-theoretic Topology (Kunen K. and Vaughan J.E., eds.), Elsevier Science Publishers B.V., North Holland (1984). MR 0776620 | Zbl 0559.54003
[11] Juhàsz I.: Cardinal functions in topology - ten years later. Mathematical Centre Tracts 123, Amsterdam (1980). MR 0576927
[12] Kočinac Lj.: On the cardinality of Urysohn and H-closed spaces. 105-111 Proc. of the Mathematical Conference in Priština (1994). MR 1466279
[13] Veličhko N.V.: H-closed topological spaces. Amer. Math. Soc. Transl. 78 (ser. 2) (1969), 103-118.
[14] Watson S.: The construction of topological spaces: Planks and Resolutions. 675-757 Recent Progress in General Topology (Hušek M. and Van Mill J., eds.), Elsevier Science Publishers, B.V., North Holland (1992). MR 1229141 | Zbl 0803.54001
[15] Watson S.: The Lindelöf number of a power; an introduction to the use of elementary submodels in general topology. Topology Appl. 58 (1994), 25-34. MR 1280708 | Zbl 0836.54004

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