I am having problems proving this fact. A space X is contractible if and only if every map f:X to Y (Y is arbitrary) is nullhomotopic. Similarly show X is contractible iff ever map f:Y to X is nullhomotopic. In the first case if Y=X then see that the identity map on X is nullhomotopic. But Im not sure how to proceed for th ...continues
a space whose fundamental group is non-abelian
Give an example of a space whose fundamental group is non-abelian
Module Theory: Vector space over complex numbers
Problem 1. Let V be a finite-dimensional complex vector space. Then V is also a vector space over real numbers R. Show that dimV ( over R) = 2*dimV(over complex C). Hint: If B={v1, v2, ..., vn} is a basis of V over C, show that B'={v1, ..., vn, iv1, ... ivn} is a basis of V over R. Problem 2. ( extend problem1) Let L be a f ...continues
1. Do the operations and simplify. (a^-2b^3)/(x^-8y) . (a^6b^2)/(x^8y^4) 2. Do the operations and simplify. (x^2 + 8x + 16)/(x) . (x^2 - 4x)/(x^2 - 16) 3. Do the operations and simplify. (a + 5)/(25 - a^2) . (5a - 25)/(5a + 25) 4. Simplify the expression. (x2 - 36)/(x^2 - 64) ÷ (x + 6)/(x - 8) 5. ...continues
Text Book : Advance Calculus, Author: - Taylor and Menon
In page number 160 i need following questions following questions to be answered: 2, 4, 7 & 11. Please mention each and every step.
The interest rate offered on a passbook savings account is 3.78% APR compounded continuously. Another account compounds interest monthly. What should the interest rate of the second account be so that the interest earned over one year is the same as the interest earned for the first account?
