Answered: Let Y = {(a, b, c): Va² + b² + c² < 1}…

Let Y = {(a, b, c): Va² + b² + c² < 1} be a subspace of R3 with the standard topology and 0 = (0,0,0). Show that the fundamental group T, (Y, 0) is trivial.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Let Y = {(a, b, c): va? + b2 + c2 < 1} be a subspace of R3 with the standard
topology and 0 =
(0,0,0). Show that the fundamental group T, (Y, 0) is trivial.

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