Recall that the standard topology Istandard (R) on R is generated by the basis Bballs (R) = {(a, b) | a,b ≤ R, a < b}. Now, let the lower limit topology TLL on R be the topology generated by the basis C = {[a, b) | a,b ≤ R, a < b}. Show that standard (R) FLL.

Q: 2) Let V₁, V2, W be vector spaces over F. Show that the set Bil(V₁ × V₂, W) of bilinear maps is a…

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Q: Let X = Rand B=(]a,b]/ a. beR, a<b} be a basis for a topology T on X. Then Ja,b] is O neither open…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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Q: show that the discrete metric on u Vector space X+3 of eannot be obtained from a norm.

A: To Show: Show that the discrete metric on a vector space X ≠ 0 cannot be obtained from a norm.

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A: We will be using basic definition

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Q: Question (1) Given a vector space V with dim V = n, along with a spanning set S = {v1,... , vk} for…

A: We will use the concept of linear independence of basis vectors.

Q: If X is a finite dimension that an inner product o Yjk = (e, ex). Can we cho fashion? %3D

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Q: Show that {|a, b): a < b}is a basis for a topology on R.

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Q: Let v1 = (1,2,1), v2 = (2,9,0), v3 = (3,3,4) . Show first that S= {v1, v2, v3} is a basis for ℝ^3.…

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Q: 2) Let V₁, V2, W be vector spaces over F. Show that the set Bil(V₁ x V₂, W) of bilinear maps is a…

A: Please check step 2 and 3 for solution.! We will verify axioms of vector space.

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A: Observe the fact  that  . Then, Now, Thus, the vector  will  not  be a  basis  vector.Let us…

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