Give the set of limit points A0 of a singleton A = {(5, 2)} on the plane R 2 with the discrete metric.

Q: Use Hahn-Banach Theorem to show that a normed linear space X is finite dimensional if its dual X' is…

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Q: Prove that any contraction between metric spaces has at most one fixed point

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Q: 3.4 Give the set of limit points Ao of a singleton A {(5, 2)} on the plane R2 with the discrete %3D…

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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.

Q: Let R be bounded by the hexagon with vertices at the points (2,0), (3,1), (3,5), (2,6), (1,5),…

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Q: Show that Loo is not icomorphic to a subepace of

A: Consider the spaces l∞   and   lp where p∈1, ∞. It is known that l∞ is not a separable space but, lp…

Q: 3) I Consider the topology = {GCR:0 ¢ Gor G = R} on R. Is open %3D %3D interval (-1, 1) compact in…

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Q: 3. Show that X = [0, 1] with the discrete metric is bounded but not totally bounded. %3D

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Q: Let H be the set of all points (x, y) in ℝ2 such that x2 + 3y2 = 12. Show that H is a closed subset…

A: Please check the answer in next step

Q: A subset I of a metric space R with the usual metric is compact if and if only it is an interval…

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Q: Show that a linear map T:X-→ Y between normed spaces is continuous if and only if {Tx,} is a Cauchy…

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Q: 3. Show that X = [0; 1] with the discrete metric is bounded but not totally bounded

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Q: Suppose that Find the Jacobian Metrix for map.

A: Given y1=x1x2-x2x4y2=x12-x42y3=x1x2x3x4

Q: Show that X = [0, 1] with the discrete metric is bounded but not totally bounded.

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Q: The set [0, 1] with the discrete metric is compact. True False

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Q: (v) Prove that if the space (X,T) has the fixed-point property and (Y, T1) is a space homeomorphic…

A: Given: v) To prove the given statement as follows,

Q: Each nonempty can be represented as the convex hull of its extreme points. --------

A: Each of the nonempty compact convex set can be represented as the convex hull of its extreme point.

Q: (K", || |,) is called the LP-norm on K". is a normed linear space for 1 <PS00. || |,

A:

Q: give an example or prove it doesn't exist j. an orientation on K44 which contains no sources or…

A: The given statement is,  An orientation on k4,4 which contains no sources or sinks but is not…

Q: Find all limit points of a set A = {(2+,2 – |n e N} on the Euclidean plane with the isual metric. Is…

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Q: A. Let H be the set of all points (x, y) in R? such that x2 + 3y2 = 12. Show that H is a closed…

A:

Q: Show that the inner product (,) on an inner product space X is a bounded sesquilinear form h. What…

A: Given that X is an inner product space with an inner product ·,· defined on it. We know that a map…

Q: A. Let H be the set of all points (x, y) in R2 such that x2 + 3y2 = 12. Show that H is a closed…

A:

Q: 2.5 Show that any interval (a,b) inR with the discrete metric is locally compact but not compact.

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Q: The set R- {0} with the usual metric is connected.

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Q: Suppose that X is the space of all (bounded or unbounded) sequences of complex unmbers and dixXx X →…

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Q: let X be a firite dimensional notm Space Then Prove that is compat.

A: As X is a finite dimensional norm space, this means that, dimX is finite.

Q: Is it possible to have a function on a metric space which is discontimuous at every point of the…

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Q: 1. Show that any interval (a,b) in R with the discrete metric is locaaly compact but not compact

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Show that the closed ball Y in a metsic SPace (X,d)is a closed set. Also, show that it (x,d) is…

A: Show that the closed ball Y in a metric space (X,d) is a closed set. also show that if (X,d) is…

Q: Show that every closed ball in R" is an n-dimensional manifold with Assuming the theorem on the…

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Q: / Let (X₁T) and (Y₁J) be top. Spaces and fix-x be a surjective and continuous map, then y is Compact…

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Q: Find all limit points of a set A = {(2+,2 – 1)|n e N} on the Euclidean plane with the usual metric.…

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Q: Prove that (R", II-|) is complete metric space.

A: This is a problem of Functional Analysis.

Q: If them every normed lineers spare X is finite demisional Linear transformation. X is bounded a

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Q: ": Prove that ( R", ||||) is complete metric space.

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Q: Prove the locally compact normal linear space is finite dimensions.

A: We have to prove the  locally compact normal linear space is finite dimensions First we define the…

Q: Example 3.16. In R with the Euclidean metric, the set [0, 1] is compact. However, note that with the…

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Q: Let R be bounded by the hexagon with vertices at the points (1,0), (2,1), (2,5), (1,6), (0,5),…

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Q: Show that closed ball in metric space (x,d) is a closed set. Also,

A: Given: (x,d) is a metric space The objective is to show that the closed ball y in (x,d) is a closed…

Q: Consider the following subsets of real plane R termine with graph: Arcwise connected A = ((x,y): 0 ≤…

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Q: Show that it A is subset of X any with the discre te metric then %3D

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Q: Let (X, t) is topological space, ACX, (X,d) is a metric space. Prove that: f: (X,d) -> (IR, Ts),…

A: Let ( X, d ) be a metric space and R with the standard topology. Then, we define a function  f(x) =…

Q: 3. Show that X = [0, 1] with the discrete metric is bounded but not totally bounded.

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Q: (b) Prove that the unit ball of a normed linear space is compact if and only if the normed linear…

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Q: Prove that R" is connected; Prove that [0, 1] × [0, 1] (with the relative topology from R²) is not…

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Q: the usual metric space defined by  d(x,y)= x-y prove the four propertis of metric space

A: Applying four properties to this metric

Q: Show the following result: Theorem. Let (X, d) be a metric space, A C X, and let u: A → R be an…

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Q: Prove the parallelogram law on an inner product space V; that is, showthatllx + Yll2 + llx - Yll2 =…

A: Prove the parallelogram law on an inner product space V; that is,  Show that…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.