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Książka Metric Spaces and Functional Spaces Jitendra Singh

Metric Spaces and Functional Spaces

Book Series P-7/24

Autor: Jitendra Singh, Preety Verma
Język: Angielski
Oprawa: Miękka
Wydawca: Independently published
Dostępność: Dostępna u dostawcy
Wysyłamy za 14-21 dni
52.77 zł
This book is crafted to support students preparing for competitive exams like the CSIR NET (JRF) in...

Informacje o książce

Autor
Jitendra Singh, Preety Verma
Język
Angielski
Oprawa
Książka - Miękka
Data wydania
2025
strony
206
EAN
9798313718705
Enbook ID
50750528
Wydawca
Independently published
Waga
284
Wymiary
152 x 229 x 11

Pełny opis

This book is crafted to support students preparing for competitive exams like the CSIR NET (JRF) in Mathematical Sciences, with a focus on metric spaces and functional analysis. Each chapter is designed to build a thorough understanding of these foundational topics.

Chapter 1: Metric Spaces and Compactness introduces the basics of metric spaces, including distance functions, open and closed sets. It then explores compactness and sequential compactness, culminating in key theorems like Bolzano-Weierstrass and Heine-Borel.

Chapter 2: Connectedness and Normed Linear Spaces covers connectedness and path-connectedness, moving to normed linear spaces. It discusses norms, Banach spaces, and completeness, providing a basis for understanding spaces of continuous functions.

Chapter 3: Metric Topology and Convergence examines metric topology, focusing on open sets, sequence convergence, and Cauchy sequences. It also addresses the concepts of completeness and the completion of metric spaces.

Chapter 4: Normed Linear Spaces and Inner Product Spaces explores properties of normed linear spaces and inner product spaces, introducing the Riesz representation theorem, which connects linear functionals with inner product spaces.

Chapter 5: Normed Linear Spaces and Compactness discusses compact operators and their properties, including the compactness of integral operators and their applications in functional analysis.

This book provides a structured approach to mastering metric and functional analysis, aimed at enhancing both exam preparation and a deeper understanding of these critical areas.

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