If X= R and d be the discrete metric Then the set of natural number (N, d) is complete no decision not complete

Q: Find all limit points of a set B = {1, }, , 1,...} on the real line with the usual metric. Is B open…

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Q: 3.2 Find all limit points of a set B = {1, },, 1, ...} on the real line with the usual metric. Is B…

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Q: 3.2 Find all limit points of a set B = {1,,, i,...} on the real line with the usual metric. Is B…

A: The objective is to find all the limit points of the Set B and to check whether B is open or closed.…

Q: C. Show that a set A in R2 is open in the Euclidean metric A it is open in the Manhattan metric.…

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Q: length of Let be an a Patch X(u,v). show that ds=Edu + 2Edudy + Gdy²

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Q: Q2. Let X = {a, b, c, d, m, n},T = {ó, X, {c}, {m,n}, {a, b, c, d}, {c, m, n}}. and Y = {b, c, m} C…

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Q: (f) The set B = {(z, y) € R? : ² + y? < 1} as a subset of R? with indiscrete metric is disconnected.…

A: As per guidelines we have to attempt 1st three parts

Q: O:- (Distance between sets) The distance DUA, B) between two nonempty Subsets A and B of metric.…

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Q: Please define these cocepts: Isolated point, .discrete topology, dense space

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Q: By using the standard metric X. on Determine JA and X\A. Justify your Justi Py answer State whether…

A: Since you have asked multiple questions, we will solve the Question Q1 (i), (a) and (b) for you. If…

Q: 16. It is a set of all points in a plane equidistant from the given point. CIRCLE SPHERE O CENTER O…

A: To choose correct option in give question.

Q: Show that d(x y) = √x-y defines a metric on the set of all real numbers

A: We will use the basic knowledge of metric spaces and set theory to answer this question.

Q: Ex: Let d is a trivial metric o space ) show that every infir

A: We have given trivial metric space d on infinite set X. We have to show that every infinite subset…

Q: Q. Let (X, B(R), µ) be a Borel measure space. If AnB=¢, BnC = 0, u(AnC) = 0. Determine µ(AUBUC).

A: Measure theory

Q: Let X and Y be two T, spaces, then X×Y. :is

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Q: Q. Let (X, B(R), µ) be a Borel measure space. If An B = A nC = BnC = 4,determine µ(AUBUC). %3D

A: Due to our guidelines we can solve only 1 question plz upload rest of questions separately.

Q: Find an example of a topological space that is seperable and first countable but not second…

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Q: Q2. Let X = {a, b, c, d, m, n}, T = {ø, X, {c}, {m,n}, {a, b, c, d}, {c, m, n}}. and Y = {b, c, m} C…

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Q: Q4. Let (X,T) be a topological space where X = {m,n, q, r} and T = {4, X, {q}, {r}, {q,r}, {m, q,…

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Q: (2) In R with the usual metric. Let A (1,3] U {4}, find: A°, A', A, g.l.b(A) and l.u.b(A).

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Q: = {a, b, c, d}, t = {Ø, X, {b, c}}. Then in the topological space (X, t), {a} = %3D %3D %3D {a, b}…

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Q: topological space a

A: Presumably, the closure of Q in R under the usual topology. It suffices to show that for every real…

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: (2) In R with the usual metric. Let A = (1,3] U{4}, find: A°, A', A, g.l.b(A) and l.u.b(A).

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Q: If X= R and d be the usual metric Then the set of natural number (N, d) is not complete no decision…

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Q: 1. Let, y eR. Determine if the following are metrics on R or not (a) d, (x, y) = /1x - y| (b)…

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

Q: Consider A = [3,7), B = (7,9] as a subset of R with the usual metric  dR (x,y) = abs(x-y). Show Ac…

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Q: M is an infinite set. If x,y ∈ M, explain the relation f below            {  1 , if x = y   f(x,y)…

A: We have to solve given problem:

Q: Suppose E ⊂ Real Numbers. With respect to the Euclidean metric, is it possible that E' = { 1/n: n ∈…

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Q: Let [a, b] be an inter a space. Let ƒ:[a,b] → X

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Q: The set [0,4] with the usual metric is sequentially compact. O True O False

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Q: The set [0,4] with the usual metric is sequentially compact.

A: We have to decide whether the given statement is true or false.

Q: IJAis dense in a metric space X. then A is closed True O False O

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Q: If X = {a, b} , how many metric can be de fined on X %3D infinite O none O only one O only finite

A: only one

Q: Consider the collection of open sets, (-n,n) from n=1 to infinity in R with the usual metric d(x,y)…

A: A metric space X is compact if every open cover of X has a finite subcover.

Q: Q. Let (X, B(R), µ) be a Borel measure space. If An BnC ¢,determine µ(AUBUC).

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Q: If X= R and d be the usual metric Then the set of irrational numbers (Q', d) is complete no decision…

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Q: Let X={9,10,11,..} and A= {10,11,12) and metric |defined on X as d(x,y) = |x-y Give the last answer

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Q: Q. Let (X, B(R), µ) be a Borel measure space. If An B= ¢, BnC = ¢,µ(Anc) = 0. Determine µ(AUBUC).…

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Q: what ordered pair is an example of a topological space that is connected but not path-connected,why?

A: We use contradiction method.

Q: 14. (Axioms of a metric) (M1) to (M4) could be replaced by other axioms (without changing the…

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Q: Task 13 Let (M, d) be a compact metric space. Show that closed subsets of M are compact.

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Q: Set of Space. d f Real number R is veeter An d is Spale

A: We know that ℝ,+ is an abelian group. Now define scalar multiplication on ℝ by α.a=αa where…

Q: show that a set of natural numbers N ,with Euclidean metric is Separable

A: We have to prove that a set of natural numbers N, with Euclidean metric is Separable.

Q: suppose X=IR with absolute %3D Value meter : Get A' and A and A° For the Yollowing set: A = : m,n EN

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Q: the function d satisfies the three condition in the definitión of metric on page 39). 3. Show that…

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