Given a set L sR", Following are true statements regarding conv L(convex hull of L):

Q: Suppose that A₁, ..., An are bounded subsets of R. Prove that A₁ U… U An is bounded and that sup(A₁…

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Q: 5. If G1,G2 be two given closed sets in a metric space (X, d) prove that: G1 U G2 is closed.

A: We have to prove given result:

Q: Show that projv u and u - projv u are orthogonal.

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Q: If J, is a 4x4 Jordan block find eit

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Q: Prove that the open ball B(a,r) is a subset of the interior of the closed ball C(a,r)

A: Given that Ba,r is an open ball of radius r and centered at a. Then a∈Ba,r                ...... (1)…

Q: det (NT) is sPace Toflogecu! and T=0U{un}such that 7Show that (N, Cl is compact slase

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Q: s paces Xand y, then both T and Ta boanded op erators are

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Q: Prove that a closed set in the metric space (S, d) either is nowhere dense in S or else contains…

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Q: Find an example of a bounded convex set S in R2 such that its profile P is nonempty but conv P ≠ S.

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Q: Let's say that a collection of open balls (Ui)ie1 = (Bx, (ri))iel in Euclidean space Rd is = UB₂,…

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Q: 6. Show that a compact metric space X is locally compact.

A: The given problem is related with metric space. We have to show that a compact metric space X is…

Q: don't understand how the equation turned into 5x+x+6/x(x+6), could you go through the equation again…

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Q: If U is homeomorphic to V and U is compact, then * V is complete O V is connected V is compact V is…

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Q: 4: state and prove L is a normed space ?

A: To prove that the space of bounded sequences, denoted as L^∞, is a normed space,we need to show that…

Q: Question Show closed bale Y in Mebic space (X,d), Alsa ఎవక is set that ? then shaw is. complete d)is…

A: Given: Y is closed ball in metric space (X, d). To show:  1. Y is closed set in (X, d). 2. If (X, d)…

Q: 3.2 Prove that in any metric space (S, d) every closed ball S,ro] is a closed set.

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Q: We say that a space (X,τ) is connected if there exist two open non-empty spaces A,B such that A∩B≠∅…

A: Let X,τ be a connected metric space. We have to show that the only subset of X are both open and…

Q: * Every Pre-Hilbert space is I - Continues Normed space -orthogonal Metric space inner Produced

A: Every pre-Hilbert Space is a complex vector space X together with an inner product (A complex inner…

Q: Show that recel projeetrue space is an manifol a.

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Q: Other Math Yes a = [5 1], b = [1 4], c = [15 3], d = [8 13] Classify each of the following…

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Q: 4.5 Prove that a closed set in the metric space (S, d) either is nowhere dense in S or else contains…

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Q: The percentage of female high school graduates who enrolled in college is given in the table below.…

A: Let x represent time(in years) since 1970, and let y represent the corresponding percentage of…

Q: Let (M, d) be a compact metric space. Show that closed subsets of M are compact.

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Q: 3.6 Prove that a closed set in the metric space (S, d) either is nowhere dense in S or else contains…

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Q: Show that close ball Y in a metfic space (X,d) is a closed set also show that if (X,d) is complete…

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

Q: Prove that a set A is countable if and only if there exist a surjection from B onto A.

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Q: Prove that a closed convex set in R" has a finite number of extreme points if and only it is the…

A: A closed convex set in ℝn has a finite number of extreme points if and only if it is the…

Q: à matric space the union of two

A: Bounded set in matric space.

Q: (b) If WCU, prove that (Recall that U+W = (c) If U + W = U, prove that WCU. U + W = U. = {u+w|u€ U₁w…

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Q: Prove that closed balls are closed sets in the standard topology on R?.

A: Topology Question

Q: thun no in

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Q: Exercise 1. Give examples of subsets A, B in a topological space X (for example X = R or X = R²)…

A: Disconnected sets

Q: 69. If S,, S, are two subsets of an inner product space V(F) then show that

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Q: bijective Show That There is map from CCA) to PCA).

A: Sol:- Let A be a set and let C(A) denote the set of all functions from A to {0,1}, which is the…

Q: Show that is not compact for the Standard topology but is compact for the cofinite topology.

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Q: let A be a set. A:=(a1,a2,a3) in R^3 such that a1 is greater than 0 but less than and equals to 1,…

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Q: Suppose that set A has 17 elements, set B has 10 elements, and their union has 18 elements. If the…

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Q: a) GR+GS b) SD + SQ c) BF +SP-AE E LL S) D B R 'С

A: Congruent Rectangle: Two rectangles are called congruent if they have the same length and breadth.…

Q: an be cauchy, prove why a subsequence of (an) must also be cauchy.

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Q: Represent the polyhedron defined by x1+x2>=1 with a minimal set of generators. Thanks !

A: According to the given information, it is required to represent the polyhedron with the minimal set…