Find a continuous function. f:D → R (where R is the real number line) such that f((x1, y1)) = f((x2, y2)) IFF (x1, y1) ∼ (x2, y2) b) What space is D/~ homeomorphic to and why?

Q: Let A = the set of straight lines in the xy-plane. Let a L b mean “line a is parallel to line 6”.…

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Q: (b) Let R = {(x, y) E R × R : 1 < ¤ < 4 or x = 6}, and S = {(x, y) E R × R : -1 < y < 1}. i. Find…

A: Solution: The given relations are R=x,y∈ℝ×ℝ : 1≤x≤4 or x=6 and S=x,y∈ℝ×ℝ : -1&lt;y&lt;1

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Q: a) Consider the following functional relation, f, defined as: f:R - R, f(x) = x Determine whether or…

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: 2) Find the indicated norms of the following linear functionals defined on RS b) f(x1,X2, X3, X4,X5)…

A: This question is about application of functional analysis

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A: No, we can write it.

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