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Base-base paracompactness and subsets of the Sorgenfrey line

Strashimir G. Popvassilev (2012)

Mathematica Bohemica

A topological space X is called base-base paracompact (John E. Porter) if it has an open base such that every base ' has a locally finite subcover 𝒞 ' . It is not known if every paracompact space is base-base paracompact. We study subspaces of the Sorgenfrey line (e.g. the irrationals, a Bernstein set) as a possible counterexample.

Borel extensions of Baire measures

J. Aldaz (1997)

Fundamenta Mathematicae

We show that in a countably metacompact space, if a Baire measure admits a Borel extension, then it admits a regular Borel extension. We also prove that under the special axiom ♣ there is a Dowker space which is quasi-Mařík but not Mařík, answering a question of H. Ohta and K. Tamano, and under P(c), that there is a Mařík Dowker space, answering a question of W. Adamski. We answer further questions of H. Ohta and K. Tamano by showing that the union of a Mařík space and a compact space is Mařík,...

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