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Characterization of σ-porosity via an infinite game

Martin Doležal — 2012

Fundamenta Mathematicae

Let X be an arbitrary metric space and P be a porosity-like relation on X. We describe an infinite game which gives a characterization of σ-P-porous sets in X. This characterization can be applied to ordinary porosity above all but also to many other variants of porosity.

A note on the three-segment problem

Martin Doležal — 2009

Mathematica Bohemica

We improve a theorem of C. L. Belna (1972) which concerns boundary behaviour of complex-valued functions in the open upper half-plane and gives a partial answer to the (still open) three-segment problem.

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