On the topological situations in geographic spaces

Abstract

As this scientific world knows very well, in Geographical Information Science (GIS), the real world is represented by spatial structure base and the representations are done through a mathematical structure between geographic elements and the properties they exhibit. This process is two layered. First one is the abstraction and conceptualization of the geographic objects. In the second layer, we should give a defence for the theory coming out at the first stage and explain the properties emerging out of the theory. Due to the diversity in the topography, the stuffs like distance, neighbourhood, proximity as well as vicinity are more or less contextual. This kind of uncertainty and imprecision can be handled with the help of topological tools. Some partial work in this direction can be seen in the literature. In this article, an attempt is made to obtain new topological structures that will help in the field of GIS. This article introduces a concept of feature relationship between objects based on topological properties. These relationships are identified through topo-geographic and metric-geographic situations and the corresponding topologies emerged out of it. The paper also introduces two new topologies: one is object oriented and the second one is feature oriented. The important structural properties and modelling capabilities are also illustrated with a simple model. Applications of the model are also briefly discussed. The prominent characteristics of the proposed theory comprises the importance of topology for representing the geographical objects through their features facilitating the integrated visualization. The abstractions of characterized objects are being again justified through this work. Of course, some restrictions are imposed in developing the theory for ensuring the scope for the realistic model. The approach shall be definitely a good step forward to strengthen the mathematical pillars of GIS.

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