The Fourier series expansion of the given function on the given interval and also find the number to which it converges at a point of discontinuity of function.

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Chapter 12.2, Problem 2E

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To find: The Fourier series expansion of the given function on the given interval and also find the number to which it converges at a point of discontinuity of function.

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1. Give a subset that satisfies all the following properties simultaneously: Subspace Convex set Affine set Balanced set Symmetric set Hyperspace Hyperplane 2. Give a subset that satisfies some of the conditions mentioned in (1) but not all, with examples. 3. Provide a mathematical example (not just an explanation) of the union of two balanced sets that is not balanced. 4. What is the precise mathematical condition for the union of two hyperspaces to also be a hyperspace? Provide a proof. edited 9:11