Give an example of weak equivalence which is not a homotopy equivalence. Let G be a finite group. Suppose that \phi: G \rightarrow S_4 is a homomorphism and \phi s onto. a) Prove that G is not abelian. b) Prove that G contains an element of order 4. ...
Imporatant:Basically, the general rule isa>b⇒f(a)>f(b)ifff(x)is an increasing functionotherwisea>b⇒f(a)<f(b)ifff(x)is a decreasing function. Using this statement, we can derive all the above given bulleted points. For exam...
Find an example of a disconnected set whose closure is connected. 5. (4pts) Explain why \lim_{\left ( x,y \right )\to \left ( 0,0 \right )}\left ( \frac{3xy^{2{x^{2}+y^{4 \right ) doesn't exist...