Question 7. Let (x,r) topological space and A, BcX. Determine be a whether A-B2A-B or not.

Q: Question 6. Let (X,7) be a topological space and A, BC X. Determine whether (A- B) CA -B or not.

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

Q: 2. Let (S, d) be a discrete metric space and p E S. Identify S i(P), S1 (p), S2(p).

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Q: QUESTION 8 The set M with the usual metric is connected. 2 O True O False

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Question 7. Let (X,r) be a topological space and A, BCX, Determine whether A-B2A-B or not.

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Q: Question 9. Prove or disprove. If (X,7,) and (X,r,) are T,-spaces, then (X,7,nt,) is also a T -…

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Q: Question 3. Consider the topology r= {X,ø,{a},{a,c},{a,b,d}} X = (a,b,c,d). Let A= {a,d}, find A and…

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Q: - Let (X, t) be a topological space and A, BCX, then 1- A° 2 A- b(A) 2- A° # A- b(A) 3- A° = A –…

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Q: Problem 2. Let X be a countable set and let s e X. Consider the particular point topology Tp on X,…

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Q: Question 2. Let (X,r) be a topological space and let A be a subset of X. Determine whether the…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

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

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Q: let and be nonempty metric Space x E X. Ihen A B Sebsets of and let d(x, A), dlA, B) and dlA) are…

A: As per bartleby guidelines for more than three subparts in a question only first three should be…

Q: Let (R, d) be the metric space with d(x,y) = |x – yl. Then the open ball B(1,2) is None of these O…

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

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Q: Question 4 . Let (X, d) be a metric space and let p(r, y) is complete if and only if (X, p) is…

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Q: Q. Assume that (X,T) is a topological space. If A = {m, n, p} CX is a closed set. Then one of the…

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Q: Question 2. Let (X,r) be a topological space and let A be a subset of X. Determine whether the…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: 5. If мая abstract manifolds, PEM. f a) Define TpM and dfp, where M²₂N is smooth map beton by dfp:…

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Q: Question 4. Let A be a subset of a topological space (X,r). Prove that the following statements are…

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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: Theorem 2.55. Let X and Y be spaces, A c Х, В С Ү, апd give X x Y the product topology. Then Aх В %3…

A: Product topology :Let X,Tx and Y,TY are two topological spaces, then product topology on X and Y is…

Q: Question 1. Let ACX. Show that 1= {UcX:AcU}U{®} is a topology on X.

A: For a set X having certain collection of subsets represented by τ will be a topology on X if it…

Q: Question 1. Let (X,7) be a topological space and let F be the collection of all closed sets, Show…

A: Closed Sets: A subset of a topological space is said to be closed if the set is open De Morgan's…

Q: QUESTION 8 The set M= EN: X< with the usual metric is connected. O True O False

A: Since you have asked more than one question. So we will solve first one for you. If you want other…

Q: QUESTION 16 The set S=fxER:x² -4<0} with the usual metric is O A. Compact. O B. connected. OC Not…

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Q: Theorem 7.33. Let X and Y be topological spaces. The product topology on X × Y is the coarsest…

A: According to the given information,

Q: Question 9. Prove or disprove. If (X,7,) and (X,r,) are T, -spaces, then (X,7,nt,) is also a T, -…

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Q: Q # 3(b) Let (G, H) be a disconnection of a topological space (X, 7), ant let AC X. If A is…

A: Before going to this proof, we prove the below statement which in turn proves the above result.…

Q: • Problem 1. Let (V, (-|·)) be an inner product space. Show, for all v, w E V, that |(v\w)| <…

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Q: Question 1. Let (X,r) be a topological space and let A be a subset of X. Determine whether the…

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Q: Question 1. Let AcX. Show that t= {Uc X :ACU}U{ø} is a topology on X.

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

Q: Question 6. Let (X,r) be a topological space and A, BCX. Determine whether (A-B)CA -B or not.

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Q: Theorem 2.22. Let A and B be subsets of a topological space X. Then: (1) A C B implies Ā c B. (2)…

A: Theorem 2.2 (i) Let A and B subsets of a topological space X such that A⊂B i.e. A is contained in B.…

Q: Question 3: (a) Show that every metric space is T2-space. (b) Describe graphically the set…

A: T2 space is also known as Hausdorff space.  Definition- A metric space X, is known as Hausdorff iff…

Q: Theorem 9.13. Let (X, d) and (Y,e) be metric spaces. Then X × Y is a metric space.

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Q: QUESTION 5 The set R/{O1 with the usual metric is not connected. O True O False

A: 5. TRUE The set, R - {0} with the usual metric can be written as the disjoint union of, (-infinity,…

Q: • Problem 1. Let (V, (-|-)) be an inner product space. Show, for all v, w e V, that |(v\w)| <…

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Q: Question 4 . Let (X,d) be a metric space and let p(x, y)=+d(x, y) d(r,y) for all r, y € X. Show that…

A: complete metric space is a metric space in which every Cauchy sequence is convergent. In other…

Q: Question (6): verse is not true. Contractible space simply connected space. But con-

A: A manifold X is Contactible if its identity map is homotopic to some constant map.   A manifold X…

Q: Let X=R and T = {]a, +oo[/a R}U{o,R}, then (X, 7) is a regular space. True False

A: This is a problem of topology.

Q: If (X, τ) is a topological space and if A,B⊂X Show that ∂(A∩B)⊂∂A∪∂B.

A: Boundary of a set in topological space: Let A be a subset of a topological space X, τ. The boundary…

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

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Q: - Consider noncoplanar points A, B, C, and D. Using three points at a time (such as A, B, and C),…

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Q: Question 2* Which one of the followings is compact a. A discrete space with at least to points. b.…

A: Given: Statements: (a) A discrete space with at least two points is compact. (b) Any set with the…

Q: Theorem 8.11. For topological spaces X and Y, X ×Y is connected if and only if each of X and Y is…

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Q: c) Let (M, d) be a metric space and let S,T≤ M. Prove that SOT = ST. But SOT SOT.

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Q: Question 1. Let (X,r) be a topological space and let F be the collection of all closed sets, Show…

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Q: Question 6. Let (X,r) be a topological space and A, BCX. Determine whether (A-B)' C A' – B* or not.

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Q: Problem 1. Let (V, {-|·)) be an inner product space. Show, for all v, w e V, that |(v\w)| <…

A: Given: V,·|· is an inner product space.   To show: For all v,w∈V, v|w≤v|v12w|w12

Q: Let X= (3, 5] u {6,7,...} and A= {5,6,7} and metric defined on X as d(x,y) = |x - y|

A: Note: As per bartleby instruction when more then three questions for subpart is given only three…

Q: Question 3: Let (M, d) be a discrete metric space. Give explicitly a simplified expression for the…

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