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On Mazurkiewicz sets. (English) Zbl 1052.54030
A Mazurkiewicz set \(M\) is a subset of the plane with the property that each straight line intersects \(M\) in exactly two points.
In the paper under review, the original construction, see [S. Mazurkiewicz, C. R. Soc. de Varsovie 7, 382–383 (1914)], is modified to obtain a Mazurkiewicz set which does not contain vertices of an equilateral triangle or a square. This answers questions given in [L. D. Loveland and S. M. Loveland, Houston J. Math 23, 485–497 (1997; Zbl 0919.54025)]. Also, similar methods are used to construct a bounded noncompact, nonconnected generalized Mazurkiewicz set.

MSC:
54G20 Counterexamples in general topology
54F15 Continua and generalizations
54B20 Hyperspaces in general topology
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