کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661498 | 1344431 | 2006 | 22 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Countable connected Hausdorff and Urysohn bunches of arcs in the plane
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In this paper, we answer a question by Krasinkiewicz, Reńska and Sobolewski by constructing countable connected Hausdorff and Urysohn spaces as quotient spaces of bunches of arcs in the plane. We also consider a generalization of graphs by allowing vertices to be continua and replacing edges by not necessarily connected sets. We require only that two “vertices” be in the same quasi-component of the “edge” that contains them. We observe that if a graph G cannot be embedded in the plane, then any generalized graph modeled on G is not embeddable in the plane. As a corollary we obtain not planar bunches of arcs with their natural quotients Hausdorff or Urysohn. This answers another question by Krasinkiewicz, Reńska and Sobolewski.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 153, Issue 11, 1 May 2006, Pages 1895-1916
Journal: Topology and its Applications - Volume 153, Issue 11, 1 May 2006, Pages 1895-1916