On Mazurkiewicz sets
Marta N. Charatonik; Włodzimierz J. Charatonik
Commentationes Mathematicae Universitatis Carolinae (2000)
- Volume: 41, Issue: 4, page 817-819
- ISSN: 0010-2628
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topCharatonik, Marta N., and Charatonik, Włodzimierz J.. "On Mazurkiewicz sets." Commentationes Mathematicae Universitatis Carolinae 41.4 (2000): 817-819. <http://eudml.org/doc/248649>.
@article{Charatonik2000,
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.},
author = {Charatonik, Marta N., Charatonik, Włodzimierz J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Mazurkiewicz set; GM-set; double midset property},
language = {eng},
number = {4},
pages = {817-819},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On Mazurkiewicz sets},
url = {http://eudml.org/doc/248649},
volume = {41},
year = {2000},
}
TY - JOUR
AU - Charatonik, Marta N.
AU - Charatonik, Włodzimierz J.
TI - On Mazurkiewicz sets
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 4
SP - 817
EP - 819
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.
LA - eng
KW - Mazurkiewicz set; GM-set; double midset property
UR - http://eudml.org/doc/248649
ER -
References
top- Kulesza J., A two-point set must be zerodimensional, Proc. Amer. Math. Soc. 116 (1992), 551-553. (1992) MR1093599
- Loveland L.D., Loveland S.M., Planar sets that line hits twice, Houston J. Math. 23 (1997), 485-497. (1997) MR1690037
- Mazurkiewicz S., Sur un ensemble plan qui a avec chaque droite deux et seulement deux points communs, C.R. Soc. de Varsovie 7 (1914), 382-383. (1914)
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