10. If t={X,Ø,{2,4),{1,4},(1,2,4},{4}} is a topology on X={1,2,3,4}, let A={2}, then the closure of A is: O {2,3} {1,2.3} (2)

Q: Let R be equipped with the Euclidean topology T and let Y =[10,20]. We denote by Ty the induced…

A:

Q: Choose the correct answer and attach the details of your work. 1. Let X = {1,2, 3, 4}. A topology on…

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

Q: Let X={a,b,c} and Y={1,2,3} and t={Y,¤,{1,2}}. The function f={(a,1),(b,3),(c,2)}. Then the topology…

A:

Q: Let X:= (a, b.c), n=(1,2,3.4), Ty:= (0,Y, {1,3), [3,4}, {3), [1,3,4}}. Let fx-Y. f:= {(a,3). (b, 3).…

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Q: 2. Let X = {1,2, 3, 4} and let T = {ó, X, {1}, {3},{1,3}} be a topology on X, then {2, 4} is a. open…

A: Since you have asked multiple question , as per our guidelines we are supposed to answer only one…

Q: Let X = {1,2, 3, 4} and let T = {, X, {1}, {3},{1,3}} be a topology on X, then {2, 4} is a. open in…

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Q: Let X = {1, 2, 3, 4, 5, 6} and let T1 = {X, 0, {3}, {1,2,3}, {2,3,4}, {2}} and T2 = {X, p, {2},…

A: T2 is a topology but T1 is not

Q: and C) Define the neighborhood system. If X=(e₁,e₂,ez.e. es. e) T= {p,X, (e), (e₂). (e₁,e₂), (e₁,e).…

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Q: 15. If t={X,Ø,{1,4},{4,3},{1,4,a},{b}} is a topology on X-{1,2,3,4}, then: * a=4, b=2 O a=3, b=1 O…

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Q: (a) Consider the following topology of X = {a,b, c, d, e}: T = {X, 0, {a}, {c, d}, {a, c, d}, {b, c,…

A: In topology and related branches of mathematics, a connected space is a topological space that…

Q: Let X:= {a, b, c}, Y:= {1,2,3,4}, Ty: = {0, Y,{1,3}, {3,4}, {3}, {1,3,4}}. Let f:X → Y, f:= {(a, 3),…

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Q: Let X = {1,2, 3, 4}. A topology on X is a. T = {6, X, {1}, {2}} b. T = {ó, X, {1}, {3,4}} c. T3 =…

A: Explanation of the answer is as follows

Q: 2. Let X = {a, b, c, d, e, f}. Which of the following collections of subsets of X is a topology on…

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Q: 3.5 Show that the metric space (R, d), where d(r, y) = |x – y|, is separable.

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

Q: 5. If r = (r, (x, y, z) and ro = (xo, Yo, 20), describe precisely the set of all points (r, y, z)…

A: We plug the given values in the given equation and simplify

Q: Let X = (1, 2, 3, 4, 5, 6) and let T1= (X, 4, {3}, (1,2,3), (2,3,4), {2}} and T2 = {X, 4, (2),…

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

Q: Let X = {a, b, c}, T1 = {X, p, {a}, {b}, {a,b}} and T2 = {X, p, {a}, {c}, {a,c}}. Then one of the…

A: Given that set X={a,b,c}

Q: The set S = {T, (U) | U is open in X} U {T, (V ) | V is open in Y } is a subbasis for the product…

A: The given theorem is related with the topic product topology. Given that S = π1-1U | U is open in X…

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: 1. Let X {1,2, 3, 4}. A topology on X is a. T = {6, X, {1}, {2}} b. T = {6, X, {1}, (3, 4}} c. T3 =…

A: As this is a multiple type question, according to the Bartleby Answering Rule, only first  question…

Q: {X, Ø, {1}, {2},{1,2},{1,3}}, is (X, t) a connected a) Let X = {1,2,3} with the topology t=…

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Q: 3 let X= {ab,c},B =} {n,b}, {9c3}.5how that Whether B is a %3D %3D base for any topology on X or not

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Q: 1. Let X = {1,2, 3, 4}. A topology on X is a. T = {0, X, {1}, {2}} b. T = {6, X, {1}, {3,4}} c. T3 =…

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Q: Let (X, T) be a topological space, AcX, then A'next (A) = 10 AO

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Q: Let X = {1,2, 3, 4} and let T {ø, X, {1}, {3},{1,3}} be a topology on X, then {2, 4} is a. open in…

A: Our objective is to choose the correct answer

Q: Let X = {1, 2, 3, 4, 5, 6} and let T1 = {X, , {3}, {1,2,3}, {2,3,4}, {2}} and T2 = {X, þ, {2},…

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Q: 13. If t={X,Ø,{2,4},{1,4},{1,2,4},{4}} is a topology on X={1,2,3,4}, let A={1,3,4}, then Int(A)= *…

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Q: Let R be equipped with the Euclidean topology T and let Y =]10,2O[. We denote by Ty the induced…

A:

Q: 2. Let X = {1,2, 3, 4} and let T = {ó, X, {1}, {3}, {1,3}} be a topology on X, then {2,4} is %3D a.…

A: Given X = 1 , 2 , 3 , 4 and T = ∅ , X , {1} , {3} , {1 , 3} is a topology on X Then open sets of (X…

Q: 1. Let X = {1,2, 3, 4}. A topology on X is a. T = {ø, X, {1}, {2}} b. T2 = {6, X, {1}, {3, 4}} c. T3…

A:

Q: (3) In R² with the standard topology: {(x, y) | x² + y² {(x, y) | x² + y? > 1}. = 1}, {(x, y) | x² +…

A: In a topological space R2with standard topology. A  subset O is open if at each point x in O there…

Q: 1. Let T and S be topologies in X. Show that SnT is also a topology in X.

A: 1.

Q: Let X = {a, b, c}, T1 = {X, 0, {a}, {b}, {a,b}} and %3D T2 = {X, p, {a}, {c}, {a,c}}. Then one of…

A: let X be a set and let τ be a family of subsets of X. Then τ is called a topology on X if:   a) Both…

Q: 10 What are the coordinates of the point on the directed line segment from K(-5,-4) to L(5, 1) that…

A: We have to find out coordinates

Q: Let Z be with the co-finite topology If A = {1,3,5, 7,.. }, then A A O O O

A: As Z is with co-finite topology. Every open neighborhood of an infinite set must contain infinitely…

Q: 1- Suppose that ,p) is a meric space, an that E CX. Then the interior E is open (m X) and the…

A: The given question is related to metric spaces. The solution is explained below.

Q: 1) 1 let X = {i,Q,3,4} woith topology T- {0,{17u3} f64}{4},x} What What the closed sets the of…

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Q: (b) A = (0, 1] in the finite-complement topology on R. (c) A= {a, c} in X = {a, b, c} with topology…

A: The interior of a subset S of a topological space X is the union of all subsets of S that are open…

Q: Let X = {1, 2, 3, 4, 5, 6} and let T1 = {X, p, {3}, {1,2,3}, {2,3,4}, {2}} and T2 = {X, ¢, {2},…

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Q: 2. Let T be the cofinite topology on R, and let A = (-x, 1) U (1, ), B = (1,2). Fine the boundary…

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Q: 3. If X = {a, b, c, d, e, f} and T is the discrete topology on X, which of the following statements…

A: True statements are: (a), (d), (g), (i), (l), (o).

Q: (2.2) Let C = {a, b, c, d} and T = {0, {a, b, c} , {b, c} , {a},C} be the topology defined on C. %3D…

A:

Q: 2. Let X = {1,2, 3, 4} and let T = {ø, X, {1}, {3}, {1,3}} be a topology on X, then {2, 4} is a.…

A: b. closed in (X,T)

Q: Consider X = {a1, a2, ..., an} Can a topology of X with 3 open and one with 4 open be equivalent?

A: We have to verify the given statement.

Q: Let X = {1, 2, 3, 4, 5, 6} and let T1 = {X, %3D 4, {2}, {1,2}, {2,3,4}, {1, 2,3,4}} and T2 = {X, þ,…

A: If T is the topology on Set X then T contains all subsets of X.

Q: Let T = {X. Ø, {b}, {a, b}} be a topology on X = {a,b,c} and let A = {a,b,c}, B = {a,b,c}. Find a)…

A: Given That: Let T={X,ϕ,{b},{a,b}} be a Topology on X={a,b,c} A={a,b,c} ,B={a,b,c} To Find: a)…

Q: 4. Let X= {a,b,c} with the topology r ={X,ø,{a},{b},{c},}{a,b},{a,c},{b,c}}. Verify whether X is…

A: Given data X=a,b,c with the topology,  τ=X,ϕ,a,b,c,a,b,a,c,b,c

Q: Let X = {a, b, c}, T1 = {X, 0, {a}, {b}, {a,b}} and T2 = {X, 6, {a}, {c}, {a,c}}. Then one of the…

A: According to experts guidelines of bartleby i have to solve only first problem so repost for further…

Q: 10. Prove that the set H={[,ne subgroap of GL(2, R). For show that x HxcH but xHx+H. :9 GL(2,R),

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Q: 3. Find a minimally invariant set in (C, R) that contains the circle [2 -(1+21)| = 4.

A: It is given that z-1+2i=4. Note that, z=x+iy. Substitute z=x+iy in z-1+2i=4:…