Marta N. Charatonik, W\l odzimierz J. Charatonik
On Mazurkiewicz sets

Comment.Math.Univ.Carolinae 41,4 (2000) 817-819.

Abstract:A Mazurkiewicz set $M$ is a subset of a plane with the property that each straight line intersects $M$ in exactly two points. We modify the original construction to obtain a Mazurkiewicz set which does not contain vertices of an equilateral triangle or a square. This answers some questions by L.D. Loveland and S.M. Loveland. We also use similar methods to construct a bounded noncompact, nonconnected generalized Mazurkiewicz set.

Keywords: Mazurkiewicz set, GM-set, double midset property
AMS Subject Classification: Primary 54C99, 54F15, 54G20; Secondary 54B20

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