Get A mathematical gift, 1, interplay between topology, PDF

By Kenji Ueno, Koji Shiga, Shigeyuki Morita

ISBN-10: 0821832824

ISBN-13: 9780821832820

This ebook will convey the sweetness and enjoyable of arithmetic to the school room. It deals critical arithmetic in a full of life, reader-friendly type. integrated are routines and plenty of figures illustrating the most techniques.

The first bankruptcy offers the geometry and topology of surfaces. between different issues, the authors speak about the Poincaré-Hopf theorem on serious issues of vector fields on surfaces and the Gauss-Bonnet theorem at the relation among curvature and topology (the Euler characteristic). the second one bankruptcy addresses a number of elements of the idea that of measurement, together with the Peano curve and the Poincaré method. additionally addressed is the constitution of three-d manifolds. particularly, it really is proved that the 3-dimensional sphere is the union of 2 doughnuts.

This is the 1st of 3 volumes originating from a sequence of lectures given via the authors at Kyoto college (Japan).

Show description

Read Online or Download A mathematical gift, 1, interplay between topology, functions, geometry, and algebra PDF

Best topology books

Download e-book for iPad: A Topological Picturebook by George K. Francis

Goals to inspire mathematicians to demonstrate their paintings and to assist artists comprehend the tips expressed by way of such drawings. This publication explains the photo layout of illustrations from Thurston's global of low-dimensional geometry and topology. It offers the rules of linear and aerial point of view from the point of view of projective geometry.

Read e-book online Cyclic Homology in Non-Commutative Geometry PDF

This quantity includes contributions through 3 authors and treats elements of noncommutative geometry which are with regards to cyclic homology. The authors supply particularly entire bills of cyclic conception from diversified and complementary issues of view. The connections among topological (bivariant) K-theory and cyclic concept through generalized Chern-characters are mentioned intimately.

New PDF release: Differential Topology, Foliations, and Group Actions:

This quantity includes the lawsuits of the Workshop on Topology held on the Pontif? cia Universidade Cat? lica in Rio de Janeiro in January 1992. Bringing jointly approximately one hundred mathematicians from Brazil and world wide, the workshop coated numerous subject matters in differential and algebraic topology, together with crew activities, foliations, low-dimensional topology, and connections to differential geometry.

Get Elementary Topology: Problem Textbook PDF

This textbook on common topology includes a certain creation to common topology and an advent to algebraic topology through its such a lot classical and easy section headquartered on the notions of basic crew and overlaying area. The e-book is adapted for the reader who's decided to paintings actively.

Additional info for A mathematical gift, 1, interplay between topology, functions, geometry, and algebra

Sample text

Since (xn ) does not converge, the sequence (yn ) also does not converge. Then the sets {xn ∶ n ∈ N} and {yn ∶ n ∈ N} are near in the metric proximity but far in the fine proximity, a contradiction. (b) If Y is uniformly discrete for some ε > 0, then, for each n ∈ N, there are distinct points xn , yn ∈ Y such that 0 ≤ d(xn , yn ) ≤ n1 . Then the sets {xn ∶ n ∈ N} and {yn ∶ n ∈ N} are near in the metric proximity. However, since Y has no limit points, they are far in the fine proximity, a contradiction.

The set N of natural numbers is near the set E = {n − n1 ∶ n ∈ N} but the image sets f (N) and f (E) are far from each other, since the gap functional on them equals inf {∣n2 − (n − n1 )2 ∣} = 2. However, the following important result is true (its utility will be shown later). 4. Let (X, d), (Y, d′ ) be metric spaces. Assume X has fine proximity δ0 and Y has any compatible proximity λ and let f ∶ X → Y be a function from X to Y . Then f is continuous, if and only if, f is proximally continuous.

If f is an isometry from space X onto Z, then X is said to be isometrically embedded into Y . Metric Space Completion: Completion of a metric space X is accomplished by isometrically embedding X onto a subset of a metric space known to be complete and then take its closure. Use the fact that R is a complete metric space. Then show that the space C ∗ (X) of bounded, realvalued, continuous functions with the sup metric d′ is complete. The final step is to embed X isometrically into C ∗ (X). 23. The metric space (C ∗ (X), d′ ) is complete.

Download PDF sample

A mathematical gift, 1, interplay between topology, functions, geometry, and algebra by Kenji Ueno, Koji Shiga, Shigeyuki Morita

by Donald

Rated 4.20 of 5 – based on 13 votes

About admin