Invitation to real analysis

by Silva, César Ernesto

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Title Statements

Full title :Invitation to real analysis / Cesar E. Silva.

Edition Statements

Publication Date:2019

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence, Rhode Island
Language:eng
Publication Date:2019

The Physical Object

Description:x, 303 pages ; : 27 cm.

Edition Identifiers

ISBN:9781470449285, 1470449285
oclc:on1080248854
LC Classification:QA300
Dewey Decimal:515/.83

Machine generated contents note: ch. 0 Preliminaries: Sets, Functions, and Induction -- 0.1. Notation on Sets and Functions -- 0.2. Basic Logic: Statements and Logical Connectives -- 0.3. Sets -- 0.4. Functions -- 0.5. Mathematical Induction -- 0.6. More on Sets: Axioms and Constructions -- ch. 1 The Real Numbers and the Completeness Property -- 1.1. Field and Order Properties of R -- 1.2.Completeness Property of R -- 1.3. Countable and Uncountable Sets -- 1.4. Construction of the Heal Numbers -- 1.5. The Complex Numbers -- ch. 2 Sequences -- 2.1. Limits of Sequences -- 2.2. Three Consequences of Order Completeness -- 2.3. The Cauchy Property for Sequences -- ch. 3 Topology of the Real Numbers and Metric Spaces -- 3.1. Metrics -- 3.2. Open and Closed Sets in R -- 3.3. Open and Closed Sets in Metric Spaces -- 3.4.Compactness in R -- 3.5. The Cantor Set -- 3.6. Connected Sets in R -- 3.7.Compactness, Connectedness, and Completeness in Metric Spaces -- ch. 4 Continuous Functions

Note continued: 4.1. Continuous Functions on R -- 4.2. Intermediate Value and Extreme Value Theorems -- 4.3. Limits -- 4.4. Uniform Continuity -- 4.5. Continuous Functions on Metric Spaces -- ch. 5 Different…

Subjects

Analyse mathématique Mathematical analysis Nombres réels Numbers, Real Real functions -- Functions of one vari… Real functions -- Functions of one vari… Real functions -- Functions of one vari… Real functions -- Functions of one vari… Real functions -- Instructional exposit…