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基于点集拓扑学的地物演化数学模型及应用研究

Research on Mathematical Model of Geo-object Evolution and Its Application Based on Point Set Topology

测绘观察 / 2020,2(2)：69-83 / 2020-05-28 1899 3173

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• 作者： 钟业勋¹²      叶彤¹*      胡宝清²     
• 单位：

  1．海军工程大学导航工程系，武汉；
  2．南宁师范大学 / 北部湾环境演变与资源利用省部共建教育部重点实验室 / 广西地表过程与智能模拟重点实验室，南宁

• 关键词： 地物；演化；基本点集；结构点集；数学模型
• Geo-object; Evolution; Based point set; Construction point set; Mathematical model
• 摘要： 物质存在与空间和时间有不可分割的联系。在时间中存在的事物，必 然在时间算子的作用下演化，这种演化具有普遍性。不同性质的地物，实质上 是不同性质的点集，因而可用点集拓扑学的相关理论，阐释地物演化问题。地 物演化中新生地物必然覆盖着消亡的地物，地物的消长的代数和恒为零是地物 演化遵循的规律。地物的消长具有同时性和渐进性。拓扑空间 X 上，结构点集 的消长必然引起相关的基本点集的量变、质变和结构的改变，这些变化也就是 目标点集Y上的演化。用实例阐述了地物演化的一般模式和由X演化为Y的程序。
• It is can not cut apart for the relation of material exists in space and time. Existed matter in time certainly occurs evolution under time operator affects and these evolution is universal. The substance of geo-object of different quality is the point set of different quality, thus the question of geo-object evolution can be expounded by the related theory of point set topology. The newborn geo-object certainly covered the disappeared geo-object and algebraic sum identically equal zero of geo-object of disappear and increase in geo-object evolution. The disappearance and increase of geo- object have the quality of at the same time and advance. The disappear and increase of construction point set certain lead to variation of quantity , mass and construction of relation based point set on the topological space X, these variation exactly the evolution on target point set Y. The authors expounded the general mode of geo-object evolution and evolution order from X to Y with an example.
• DOI： https://doi.org/10.35534/go.0202010
• 引用： 钟业勋，叶彤，胡宝清．基于点集拓扑学的地物演化数学模型及应用研究［J］．测绘观察，2020，2（2）：69-83．
  https://doi.org/10.35534/go.0202010