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Keywords:
nowhere dense; point-$\kappa$ family; $\pi$-caliber
Summary:
We study the concept of $\pi$-caliber as an alternative to the well known concept of caliber. $\pi$-caliber and caliber values coincide for regular cardinals greater than or equal to the Souslin number of a space. Unlike caliber, $\pi$-caliber may take on values below the Souslin number of a space. Under Martin's axiom, $2^{\omega }$ is a $\pi$-caliber of $\mathbb{N}^{\ast}$. Prikry's poset is used to settle a problem by Fedeli regarding possible values of very weak caliber.
References:
[1] Comfort W., Negrepontis S.: The Theory of Ultrafilters. Springer, New York-Heidelberg, 1974. MR 0396267 | Zbl 0298.02004
[2] Comfort W., Negrepontis S.: Chain Condition in Topology. Cambridge Tracts in Mathematics, 79, Cambridge University Press, Cambridge-New York, 1982. MR 0665100
[3] Engelking R.: General Topology. Heldermann, Berlin, 1989. MR 1039321 | Zbl 0684.54001
[4] Fedeli A.: On the $\kappa$-Baire property. Comment. Math. Univ. Carolin. 34 (1993), 525–527. MR 1243083
[5] Fedeli A.: Weak calibers and the Scott-Watson theorem. Czechoslovak Math. J. 46 (1996), 421–425. MR 1408297 | Zbl 0879.54026
[6] Fletcher P., Lindgren W.: A note on spaces of second category. Arch. Math. (Basel) 24 (1973), 186–187. DOI 10.1007/BF01228197 | MR 0315663 | Zbl 0259.54019
[7] Jech T.: Set Theory. 2nd edition, Springer, Berlin, 1997. MR 1492987 | Zbl 1007.03002
[8] Juhasz I.: Cardinal Functions in Topology: Ten Years After. Mathematical Centre Tracts, 123, Mathematisch Centrum, Amsterdam, 1980. MR 0576927
[9] Kanamori A.: The Higher Infinite. Large Cardinals in Set Theory from their Beginnings. Perspectives in Mathematical Logic, Springer, Berlin, 1994. MR 1321144 | Zbl 1154.03033
[10] McCoy R.A., Smith J.C.: The almost Lindelöf property for Baire spaces. Topology Proc. 9 (1984), 99–104. MR 0781554 | Zbl 0559.54019
[11] Prikry K.: Changing measurable cardinals into accessible cardinals. Dissertationes Math. 68 (1970). MR 0262075
[12] Šanin N.A.: On intersection of open subsets in the product of topological spaces. C. R. (Doklady) Acad. Sci. URSS 53 (1946), 499–501. MR 0018815
[13] Šanin N.A.: On the product of topological spaces. Trudy Mat. Inst. Steklov. 24 (1948). MR 0027310
[14] Tall F.D.: The countable chain condition versus separability --- applications of Martin's Axiom. General Topology Appl. 4 (1974), 315–339. DOI 10.1016/0016-660X(74)90010-5 | MR 0423284 | Zbl 0293.54003

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