On Mazurkiewicz Sets

Author

Marta N. Charatonik
W. J. Charatonik, Missouri University of Science and TechnologyFollow

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.

Recommended Citation

M. N. Charatonik and W. J. Charatonik, "On Mazurkiewicz Sets," Commentationes Mathematicae Universitatis Carolinae, Charles University, Jan 2000.

Department(s)

Mathematics and Statistics

Keywords and Phrases

GM-set; Mazurkiewicz set; double midset property

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2000 Charles University, All rights reserved.

Publication Date

01 Jan 2000