Identifiant pérenne de la notice : 217174116
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Note publique d'information : This self-contained work on linear and metric structures focuses on studying continuity
and its applications to finite- and infinite-dimensional spaces. The book is divided
into three parts. The first part introduces the basic ideas of linear and metric spaces,
including the Jordan canonical form of matrices and the spectral theorem for self-adjoint
and normal operators. The second part examines the role of general topology in the
context of metric spaces and includes the notions of homotopy and degree. The third
and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces
and the spectral theory of compact operators. Mathematical Analysis: Linear and Metric
Structures and Continuity motivates the study of linear and metric structures with
examples, observations, exercises, and illustrations. It may be used in the classroom
setting or for self-study by advanced undergraduate and graduate students and as a
valuable reference for researchers in mathematics, physics, and engineering. Other
books recently published by the authors include: Mathematical Analysis: Functions
of One Variable, and Mathematical Analysis: Approximation and Discrete Processes.
This book builds upon the discussion in these books to provide the reader with a strong
foundation in modern-day analysis
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