Functional Analysis Answers

Describe verbally how to solve y=mx+c. What assumptions have you made about the value

of ?

If a third-degree polynomial has a lone x-intercept at x=a , discuss what this implies about the linear and quadratic factors of that polynomial

Kindly answer this as soon as possible. Urgent Elaborate each step.

Show that Euclidean space and unitary space are not compact. Explain each step. 

If (x_n) and (y_n) are sequences in the same normed space X, show that x_n→x and y_n→y implies x_n+y_n→x+y as well as αx_n→αx, where α is any scalar.

Let X and Y be normed spaces, T∈B(X,Y) and (x_n) a sequence in X. If x_n→x₀, show that Tx_n→Tx₀.

If x_n∈C[a,b] and x_n→x∈C[a,b]. Show that (x_n) is pointwise convergent on [a,b], that is, (x_n(t)) converges for every t∈C[a,b].

Let X and Y be metric spaces, X compact, and T: X →Y bijective

and continuous. Show that T is a homeomorphism.