On Mazurkiewicz Sets

Marta N. Charatonik; W. J. Charatonik

On Mazurkiewicz Sets

Marta N. Charatonik
, W. J. Charatonik

Missouri University of Science and Technology

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	Commentationes Mathematicae Universitatis Carolinae
State	Published - Jan 1 2000

Keywords

GM-set
Mazurkiewicz set
double midset property

Disciplines

Mathematics
Statistics and Probability

Access to Document

http://www.maths.tcd.ie/EMIS/journals/CMUC/

Cite this

@article{55cf727f78ab4aa08eb5324af7ef9cec,

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.",

keywords = "GM-set, Mazurkiewicz set, double midset property",

author = "Charatonik, \{Marta N.\} and Charatonik, \{W. J.\}",

year = "2000",

month = jan,

day = "1",

language = "American English",

journal = "Commentationes Mathematicae Universitatis Carolinae",

}

TY - JOUR

T1 - On Mazurkiewicz Sets

AU - Charatonik, Marta N.

AU - Charatonik, W. J.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - 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.

AB - 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.

KW - GM-set

KW - Mazurkiewicz set

KW - double midset property

UR - https://scholarsmine.mst.edu/math_stat_facwork/403

UR - http://www.maths.tcd.ie/EMIS/journals/CMUC/

M3 - Article

JO - Commentationes Mathematicae Universitatis Carolinae

JF - Commentationes Mathematicae Universitatis Carolinae

ER -

On Mazurkiewicz Sets

Abstract

Keywords

Disciplines

Access to Document

Other files and links

Fingerprint

Cite this