Closed Linear Operator

(See attached file for full problem description) --- If the inverse of a closed linear operator T exists, show that is a closed linear operator.

Closed Linear Operator

(See attached file for full problem description) Let T be a closed linear operator with domain in a Banach space X and range in a normed space Y. If exists and is bounded, show that is closed.

In the real world, what might be a situation where it is preferable for the data to form a relation but not a function?

There is a formula that converts temperature in degrees Celsius to temperature in degrees Fahrenheit. You are given the following data points: Fahrenheit Celsius Freezing point of water 32 0 Boiling point of water 212 100 Find the linear equation that expresses temperature in degrees Fahrenheit as a function of temperature in degrees Celsius. Find the linear equation that expresses temperature in degrees Celsius as a function of temperature in degrees Fahrenheit. How do the graphs of these two functions differ? Do not just list the functions. You must show all of the steps you used to derive the functio... click for more

Minimization Problem

(See attached file for full problem description)

Urgent

Please help. I only need answers with brief explanations. No need of detailed working. (See attached file for full problem description) --- State whether the following are true or false with reasons: 1. If a in S6, then an =1 for some n greater than or equal to 1. 2. If axa-1=bxb-1, then a=b 3. The function e:N x NN, defined by e(m,n)=mn is an associative operation. 4. Every infinite group contains an element of infinite order. 5. Let G be a finite group in which every element has a square root; that is, for each x in G, there exists y in G with y=x2. Prove that every element in G has a unique square root. 6. If H is a subgroup of K and K is a subgroup of... click for more