On Diagrams Representing Maps
On Diagrams Representing Maps
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关于表示地图的图表
DOI：
10.1112/jlms/s1-28.3.336
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发表时间：
1953
影响因子：
1.2
通讯作者：
P. Ungar
中科院分区：
文献类型：
--
作者：
P. Ungar
平面图是一组非重叠区域a、B、..在由表现良好的简单曲线界定的平面中，a与B相邻或a 16意味着a和b的边界有一条公共弧线。ab表示闭集a和B的公共点。如果两个映射的区域可以1-1对应，使得相邻对对应于相邻对，则称这两个映射是同构的。我们将用破折号区分同构中的相应区域。我们称一个映射为饱和映射，如果它具有下列性质：（i）它由有限个覆盖整个平面的区域组成;（ii）只有一个区域是无限的;（iii）至多有3个区域在任一点相交;（iv）每个区域是单连通的;（v）任何两个相邻区域的并是单连通的;（vi）对于任何两个区域a和B，ab要么是单弧要么是空的。
A plane map is a set of non-overlapping regions a, b,... in the plane which are bounded by well-behaved simple curves, a is adjacent to b or a 16 means that the boundaries of a and 6 have a common arc. ab denotes the common points of the closed sets a and b. Two maps are said to be isomorphic if their regions can be put into 1-1 correspondence so that adjacent pairs correspond to adjacent pairs. We shall distinguish corresponding regions in an isomorphism by dashes. We call a map saturated if it has the following properties:(i) it consists of a finite number of regions whioh cover the whole plane;(ii) only one region is infinite;(iii) at most 3 regions meet at any point;(iv) every region is simply connectedf;(v) the union of any two adjacent regions is simply connected;(vi) for any two regions a and b, ab is either a simple arc or empty.