| Title:
|
On Mazurkiewicz sets (English) |
| Author:
|
Charatonik, Marta N. |
| Author:
|
Charatonik, Włodzimierz J. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
817-819 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Mazurkiewicz set |
| Keyword:
|
GM-set |
| Keyword:
|
double midset property |
| MSC:
|
54B20 |
| MSC:
|
54C99 |
| MSC:
|
54F15 |
| MSC:
|
54G20 |
| idZBL:
|
Zbl 1052.54030 |
| idMR:
|
MR1800162 |
| . |
| Date available:
|
2009-01-08T19:07:41Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119213 |
| . |
| Reference:
|
[1] Kulesza J.: A two-point set must be zerodimensional.Proc. Amer. Math. Soc. 116 (1992), 551-553. MR 1093599 |
| Reference:
|
[2] Loveland L.D., Loveland S.M.: Planar sets that line hits twice.Houston J. Math. 23 (1997), 485-497. MR 1690037 |
| Reference:
|
[3] 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. |
| . |
