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A topological version of the famous Hedetniemi conjecture says: The mapping index of the Cartesian product of two Z / 2 - spaces is equal to the minimum of their Z / 2 -indexes. The main purpose of this article is to study the topological version of the Hedetniemi conjecture for G-spaces. Indeed, we show that the topological Hedetniemi conjecture cannot be valid for general pairs of G-spaces. More precisely, we show that this conjecture can possibly survive if the group G is either a cyclic p-group or a generalized quaternion group whose size is a power of 2. [ABSTRACT FROM AUTHOR]

The article reviews the methodology for assessing water bodies in the territories of Western and Central Kazakhstan. The concept of sustainable development of the region for recreational activities of this study is relevant. Literary sources of research of lakes of Western, Northern, and Central Kazakhstan are analyzed. The study area has excellent opportunities for the development of certain types of tourism. As a result of topographic and bathymetric surveys of water resources of geosystems, the most reliable morphometric data were obtained. Analyzing of the results of remote sensing data processing and index mapping made it possible to assess the area of lakes and determine their main metric characteristics. The article also evaluates the accuracy of the results obtained using various remote sensing materials. The geographical position of the lakes causes differences in the factors of formation of their hydrological regime. The altitude position of the studied lakes is also manifested in the peculiarity of the course of long-term changes in their characteristics. These received and processed research materials will be used for tourist and recreational activities. Recommendations on the tourist and recreational use of lake systems of Kazakhstan are given.

The article reviews the methodology for assessing water bodies in the territories of Western and Central Kazakhstan. The concept of sustainable development of the region for recreational activities of this study is relevant. Literary sources of research of lakes of Western, Northern, and Central Kazakhstan are analyzed. The study area has excellent opportunities for the development of certain types of tourism. As a result of topographic and bathymetric surveys of water resources of geosystems, the most reliable morphometric data were obtained. Analyzing of the results of remote sensing data processing and index mapping made it possible to assess the area of lakes and determine their main metric characteristics. The article also evaluates the accuracy of the results obtained using various remote sensing materials. The geographical position of the lakes causes differences in the factors of formation of their hydrological regime. The altitude position of the studied lakes is also manifested in the peculiarity of the course of long-term changes in their characteristics. These received and processed research materials will be used for tourist and recreational activities. Recommendations on the tourist and recreational use of lake systems of Kazakhstan are given. [ABSTRACT FROM AUTHOR]

The Transportation-Efficient Land Use Mapping Index (TELUMI) is a tool to visualize and to quantify micro-level metropolitan land use and development patterns as they affect travel demand. It can assist transportation and urban planning authorities in identifying zones where land use supports multimodal travel and in determining a region's transportation system efficiency. An application of the TELUMI in the Seattle region showed that residential units and employment concentrated in transportation-efficient areas covering less than 20 percent of the region. An interactive, multi-scaled tool, the TELUMI can also support scenario building to simulate land use changes that improve transportation system performance. [ABSTRACT FROM AUTHOR]