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Keywords:
cardinal functions; $\tau \theta $-closed sets; $w$-compactness degree
cardinal functions; $\tau \theta $-closed sets; $w$-compactness degree
Summary:
In this paper, two cardinal inequalities for functionally Hausdorff spaces are established. A bound on the cardinality of the $\tau \theta $-closed hull of a subset of a functionally Hausdorff space is given. Moreover, the following theorem is proved: if $X$ is a functionally Hausdorff space, then $|X|\leq 2^{\chi (X)\text{\it wcd}(X)}$.
References:
[1] Arkhangel'skii A.V.: The power of bicompacta with the first axiom of countability. Soviet Math. Dokl. 10 (1969), 951-955.
[2] Bella A., Cammaroto F.: On the cardinality of Urysohn spaces. Canad. Math. Bull. 31 (2) (1988), 153-158. MR 0942065 | Zbl 0646.54005
[3] Engelking R.: General Topology. Revised and completed edition. Sigma Series in Pure Mathematics 6, Heldermann Verlag, Berlin, 1989. MR 1039321
[4] Hodel R.: Cardinal Functions I. in Handbook of Set-Theoretic Topology (K. Kunen and J.E. Vaughan, eds.), Elsevier Science Publishers, B.V., North Holland, 1984, pp. 1-61. MR 0776620 | Zbl 0559.54003
[5] Ishii T.: On the Tychonoff functor and $w$-compactness. Topology Appl. 11 (1980), 173-187. MR 0572372 | Zbl 0441.54012
[6] Pol R.: Short proofs of two theorems on cardinality of topological spaces. Bull. Acad. Polon. Sci. Ser,. Math. Astr. Phys. 22 (1974), 1245-1249. MR 0383333 | Zbl 0295.54004
[7] Stephenson R.M., Jr.: Spaces for which the Stone-Weierstrass theorem holds. Trans. Amer. Math. Soc. 133 (1968), 537-546. MR 0227753 | Zbl 0164.53003
[8] Stephenson R.M., Jr.: Product spaces for which the Stone-Weierstrass theorem holds. Proc. Amer. Math. Soc. 21 (1969), 284-288. MR 0250260
[9] Stephenson R.M., Jr.: Pseudocompact and Stone-Weierstrass product spaces. Pacific J. Math. 99 (1) (1982), 159-174. MR 0651493 | Zbl 0426.54009
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