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The purpose of this paper is to introduce a new type of topological spaces called a double topological space defined on a bi-set. This notion is different from the bitopological space due to J. C. Kelly [8]. Also, some fundamental concepts defined on a double topological space are investigated.
Accurate mapping plays a crucial role in the management of natural hazards, particularly in the monitoring of sand dune movement. In this research, we focused on modeling sand dune encroachment in a specific study area situated between latitudes 25° 26’ 30” N and 27° 49’ N, and longitudes 27° 28’ E and 31° 08’ E, located in the central Western Desert of Egypt. To accomplish this, we employed advanced machine learning techniques, such as linear support vector machines (SVM), and integrated machine learning algorithms with spatial data types using GIS and R software. To identify dune accumulations from various multispectral sensors, we proposed a novel index called the Drifting Sand Index (DSI). The effectiveness of the DSI was demonstrated, highlighting its significant potential for mapping and monitoring dunes in the study area. Through the utilization of different data sources and field surveys, we identified approximately 150 sand dune locations in the study area. For the sand dune encroachment modeling, we generated nine variables, including slope, aspect, altitude, lithology, distance to roads, normalized difference vegetation index (NDVI), land use/land cover (LULC), wind speed, and direction and soil properties. The results obtained from the DSI indicated that the movement of dunes in the study area ranged approximately 4.9 m/yr towards the southeast. By employing the SVM model, we were able to produce a comprehensive map illustrating the risks associated with sand dune encroachment. The sand dunes hazard zones were classified into five categories: very low (47.1 km2), low (11285.7 km2), medium (356.8 km2), high (9519.1 km2), and very high-risk (16552.1 km2) zones. The area under curve (AUC) approach has been applied to evaluate, validate, and compare the SVM model performance. The results indicated that AUC values for nine MLTs range from 95.1%. The RMSE value for the applied MLT was determined to be 0.391, indicating a significant agreement between the model and reality. .The information derived from this study will contribute to the achievement of sustainable development goals and the preservation of the environment.
