showthat two metricspace s (Xyd) and (X,d) are home omorphicifand onlyifevery open battin(Xd)contains as open ball centered at the sam e pointin Exd) and con versely

Q: 2. Let D be the half-disc in the xy-plane given by x +y <9. 2. Calculate e-?+v}dA Select one: a.…

A: Let  D  be the half-disc  in the xy planegiven  by  x2+y2&lt;9calculate ∫∫D  e-x2+y2  dA

Q: Let (x,d) be metric space and A, BC X. 2. Show that (AnB)= A'n B and AUB = AUB %3D

A:

Q: -}]-=[}]»=[}- [] 3 Find Let vị = and p = 3 a hyperplane [f: d] (in this case, a line) that strictly…

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Q: Q4) Find the intersection of the line x = and the sphere x? + (y – 3)² + (z – 2)² = 4. A) (1,1,0) B)…

A: 1. In analytic geometry, a line and a sphere can intersect in three ways: No intersection at all…

Q: Let M⊂R ^ 3 be a surface and f be a diff.bilir function on this surface. Show that if Q is this…

A: Given: Let M⊂R3be a surface and let f be a differentiable function on this surface. If Q is a 1-1…

Q: Q1 find acubie palonemiat ofk given-points for27,3},(2,12)e

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Q: V=R Prooflthat Nisavectors sPoe

A: Given that V = ℝ+ Operations + and · defined as, x + y = xy rx = xr, where x,y ∈V; r ∈F To prove: V…

Q: (b) Every continuous map S? →T² is homotopic to the constant map.

A:

Q: Which of the following are suspaces of 1 2 1 R4 whereu , v = 1 -1] Select one or more: A. {w; w. v =…

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Q: Calculate | F.dr, where F(x, y) = (x²–3y)i+(ye")j and the curve and curve C is the parabola æ = y² +…

A: We have to calculate ∫CF.dr, where Fx,y=x2-3yi+yeyj and the curve C is the parabola x=y2+1 from A1,0…

Q: Show that in 3D space, (a) k EijkEpqk = δip&jq – διαδjp

A: Note:  Since you have posted multiple questions, we will solve first question for you. Kindly repost…

Q: (4) 2 What is the square of the (minimum) distance between W and P? Let W Span< = -2 be a plane in…

A: Given that

Q: Show that (Cod) is metric space

A: