Title

On Mazurkiewicz Sets

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.

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.


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