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Jan van Mill On nowhere first-countable compact spaces with countable π-weight Comment.Math.Univ.Carolin. 56,2 (2015) 237 –241.

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Jan van Mill

On nowhere first-countable compact spaces with countable π -weight

Comment.Math.Univ.Carolin. 56,2 (2015) 237 –241.

Abstract: The minimum weight of a nowhere first-countable compact space of countable

π

-weight is shown to be

κB

, the least cardinal

κ

for which the real line

R

can be covered by

κ

many nowhere dense sets.

Keywords:

π

-weight; nowhere first-countable;

κB

; compact space AMS Subject Classification: 54D35

References

[1] Juh´asz I., Cardinal Functions in Topology, Mathematical Centre Tract, 34, Mathematical Centre, Amsterdam, 1971.

[2] Juh´asz I.,On the minimum character of points in compact spaces, Topology. Theory and appli- cations, II (P´ecs, 1989), Colloq. Math. Soc. J´anos Bolyai, vol. 55, North-Holland, Amsterdam, 1993, pp. 365–371.

[3] Kunen K., Set Theory. An Introduction to Independence Proofs, Studies in Logic and the Foundations of Mathematics, 102, North-Holland Publishing Co., Amsterdam, 1980.

[4] van Mill J., On the character and π-weight of homogeneous compacta, Israel J. Math. 133 (2003), 321–338.

[5] Miller A.W.,The Baire category theorem and cardinals of countable cofinality, J. Symbolic Logic47(1982), no. 2, 275–288.

[6] Shelah S.,Covering of the null ideal may have countable cofinality, Fund. Math.166(2000), 109–136.

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