On Mazurkiewicz Sets
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.
M. N. Charatonik and W. J. Charatonik, "On Mazurkiewicz Sets," Commentationes Mathematicae Universitatis Carolinae, Charles University, Jan 2000.
Mathematics and Statistics
Keywords and Phrases
GM-set; Mazurkiewicz set; double midset property
Article - Journal
© 2000 Charles University, All rights reserved.
01 Jan 2000