EUCLIDEAN SPACE: SEQUENCES IN R^m SPACE AND IMPORTANT SETS IN R^m SPACE

• Abdullayeva Madinaxon Mamirjon Qizi

  Student of the "Mathematics and Informatics" Department, Andijan State Pedagogical Institute, Uzbekistan

Objective: This article aims to provide comprehensive insights into the Euclidean space R^m, serving as a resource for students, educators, and researchers in mathematical analysis and linear algebra. Method: Fundamental concepts and properties of R^m are elaborated, including sequences, distance properties, and the characteristics of open and closed sets. The analysis incorporates mathematical frameworks to examine bounded and unbounded sets alongside hyperplanes within R^m.  Results:  The study elucidates the key mathematical constructs and properties that define R^m, offering a structured understanding of its theoretical and practical applications in mathematics.  Novelty: This work stands out by consolidating essential definitions and properties of R^m in a single resource, bridging gaps between foundational and advanced topics in mathematical analysis.

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