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1.

図書
図書
1. Logic, sets and numbers (: pbk)
K.G. Binmore
出版情報: Cambridge [Eng.] : Cambridge University Press, 1980  x, 130 p. ; 24 cm
シリーズ名: The foundations of analysis : a straightforward introduction / K.G. Binmore ; book 1
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目次情報: 続きを見る
Introduction
Proofs / 1：
Logic (I) / 2：
Logic (II) / 3：
Set operations / 4：
Relations / 5：
Functions / 6：
Real numbers (I) / 7：
Principle of induction / 8：
Real numbers (II) / 9：
Construction of the number systems / 10：
Number theory / 11：
Cardinality / 12：
Introduction
Proofs / 1：
Logic (I) / 2：
2.

図書
図書
2. Constructive analysis (: us ; : gw)
Errett Bishop, Douglas Bridges
出版情報: Berlin ; New York : Springer-Verlag, c1985  xii, 477 p. ; 24 cm.
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 279
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3.

図書
図書
3. Foundations of mathematical analysis (:pbk.)
Richard Johnsonbaugh, W. E. Pfaffenberger
出版情報: New York, N.Y. : M. Dekker, c1981  viii, 428 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 62
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目次情報: 続きを見る
Preface
Preface to the Dover Edition
Sets and Functions / I：
Sets / 1.：
Functions / 2.：
The Real Number System / II：
The Algebraic Axioms of the Real Numbers / 3.：
The Order Axiom of the Real Numbers / 4.：
The Least-Upper-Bound Axiom / 5.：
The Set of Positive Integers / 6.：
Integers, Rationals, and Exponents / 7.：
Set Equivalence / III：
Definitions and Examples / 8.：
Countable and Uncountable Sets / 9.：
Sequences of Real Numbers / IV：
Limit of a Sequence / 10.：
Subsequences / 11.：
The Algebra of Limits / 12.：
Bounded Sequences / 13.：
Further Limit Theorems / 14.：
Divergent Sequences / 15.：
Monotone Sequences and the Number e / 16.：
Real Exponents / 17.：
The Bolzano-Weierstrass Theorem / 18.：
The Cauchy Condition / 19.：
The lim sup and lim inf of Bounded Sequences / 20.：
The lim sup and lim inf of Unbounded Sequences / 21.：
Infinite Series / V：
The Sum of an Infinite Series / 22.：
Algebraic Operations on Series / 23.：
Series with Nonnegative Terms / 24.：
The Alternating Series Test / 25.：
Absolute Convergence / 26.：
Power Series / 27.：
Conditional Convergence / 28.：
Double Series and Applications / 29.：
Limits of Real-Valued Functions and Continuous Functions on the Real Line / VI：
Definition of the Limit of a Function / 30.：
Limit Theorems for Functions / 31.：
One-Sided and Infinite Limits / 32.：
Continuity / 33.：
The Heine-Borel Theorem and a Consequence for Continuous Functions / 34.：
Metric Spaces / VII：
The Distance Function / 35.：
R[superscript n], l[superscript 2], and the Cauchy-Schwarz Inequality / 36.：
Sequences in Metric Spaces / 37.：
Closed Sets / 38.：
Open Sets / 39.：
Continuous Functions on Metric Spaces / 40.：
The Relative Metric / 41.：
Compact Metric Spaces / 42.：
The Bolzano-Weierstrass Characterization of a Compact Metric Space / 43.：
Continuous Functions on Compact Metric Spaces / 44.：
Connected Metric Spaces / 45.：
Complete Metric Spaces / 46.：
Baire Category Theorem / 47.：
Differential Calculus of the Real Line / VIII：
Basic Definitions and Theorems / 48.：
Mean-Value Theorems and L'Hospital's Rule / 49.：
Taylor's Theorem / 50.：
The Riemann-Stieltjes Integral / IX：
Riemann-Stieltjes Integration with Respect to an Increasing Integrator / 51.：
Riemann-Stieltjes Sums / 52.：
Riemann-Stieltjes Integration with Respect to an Arbitrary Integrator / 53.：
Functions of Bounded Variation / 54.：
Riemann-Stieltjes Integration with Respect to Functions of Bounded Variation / 55.：
The Riemann Integral / 56.：
Measure Zero / 57.：
A Necessary and Sufficient Condition for the Existence of the Riemann Integral / 58.：
Improper Riemann-Stieltjes Integrals / 59.：
Sequences and Series of Functions / X：
Pointwise Convergence and Uniform Convergence / 60.：
Integration and Differentiation of Uniformly Convergent Sequences / 61.：
Series of Functions / 62.：
Applications to Power Series / 63.：
Abel's Limit Theorems / 64.：
Summability Methods and Tauberian Theorems / 65.：
Transcendental Functions / XI：
The Exponential Function / 66.：
The Natural Logarithm Function / 67.：
The Trigonometric Functions / 68.：
Inner Product Spaces and Fourier Series / XII：
Normed Linear Spaces / 69.：
The Inner Product Space R[superscript 3] / 70.：
Inner Product Spaces / 71.：
Orthogonal Sets in Inner Product Spaces / 72.：
Periodic Functions / 73.：
Fourier Series: Definition and Examples / 74.：
Orthonormal Expansions in Inner Product Spaces / 75.：
Pointwise Convergence of Fourier Series in R[a, a + 2[pi] / 76.：
Cesaro Summability of Fourier Series / 77.：
Fourier Series in R[a, a + 2[pi] / 78.：
A Tauberian Theorem and an Application to Fourier Series / 79.：
Normed Linear Spaces and the Riesz Representation Theorem / XIII：
Normed Linear Spaces and Continuous Linear Transformations / 80.：
The Normed Linear Space of Continuous Linear Transformations / 81.：
The Dual Space of a Normed Linear Space / 82.：
Introduction to the Riesz Representation Theorem / 83.：
Proof of the Riesz Representation Theorem / 84.：
The Lebesgue Integral / XIV：
The Extended Real Line / 85.：
[sigma]-Algebras and Positive Measures / 86.：
Measurable Functions / 87.：
Integration on Positive Measure Spaces / 88.：
Lebesgue Measure on R / 89.：
Lebesgue Measure on [a, b] / 90.：
The Hilbert Spaces Y[superscript 2](X, M, [mu]) / 91.：
Vector Spaces / Appendix：
References
Hints to Selected Exercises
Index
Errata
Preface
Preface to the Dover Edition
Sets and Functions / I：
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