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. open in (X, T) b. closed in (X, T) c. clopen in (X, T) d. neither open nor closed

Q: 9. Let X = NU {v2, v3} be a set. Consider the topology 7 on X such that T = {AC X : ACN or if A…

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Q: 2. Let (X,r) be a topological space. Where X {a,b.c,d,e} and…

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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: 1. Let Ω = (0, ∞). Let A = (3, 8] and B = (5, 10]. Find the smallest collection of subsets of Ω that…

A: Definition: Let Ω be a non-empty set. Let Σ be a collection of subsets of Ω. The collection Σ is…

Q: * Let R be with the indiscrete topology. If A = {1,3, 5, 7, . }, then A' = A O N O RO

A: This question is related to topology, we will use the definition of indiscrete topology to solve it.

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: Exercise 1. Let X = {a, b, c, d, e}. Which of the following families is a topology? Why or why not?…

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Q: - Find the mappings taking [(0,0, 0), (1,0, 0), (0, 1,0), (0, 0, 1)] in u, v, w space to each of the…

A: Consider the given mapping U= [(0,0,0),(1,0,0),(0,1,0).(0,0,1)] in u,v,w space to  each of the…

Q: 3. Let (X, T) be the topological space defined in question 2., then the closure of {2} is a. X b.…

A: It depends on the given topological space. Here topological space is not specified. If it's usual…

Q: 4 ,3 ,2 ,1 = X آقا -X L find The Possible Topology That Contain sus { 1123 , 2, 3, {\/ 3 ، 4 seas

A: It is given that,  X = {1, 2, 3, 4}. We have to find the possible Topology on X that contain the…

Q: Show the span {(1,0, 1), (-1, 2, 3), (0, 1, – 1)} is all of R'.

A: Let x=1, 0, 1, y=-1, 2, 3 and z=0, 1, -1. We have to show that spanx, y, z is actually the vector…

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: (A,7) be the topological space defined in question 2. Let A = {1,2,3}, then the set of limit points…

A: Solution: (4) Answer: The set is  A=1,2,3 Clearly, set A is finite.  We know that a finite set does…

Q: 1. Let X = {1,2, 3, 4}. A topology on X is %3D a. T = {6, X, {1}, {2}} b. T2 = {0, X, {1}, {3, 4}}…

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Q: 6. Let's say the set X= {1, 2, 3, 4 is given as the whole space and M = {Ø,{3},{4},{1, 2},{3, 4},…

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Q: 5) Let A= (2,3) U {4} be a subset of R with the standard opology. Find Ə(A).

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Q: If X = {a, b, c} , Tx = {0, X, {a},{b, c}}, Y = {x, y, z} and ty = {Ø, Y, {y}} then f = {(a, z), (b,…

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Q: 1. Let X={a,b,c} and Y={1,2} then X×Y ={(a,1),(a,2).(b,1).(b,2),(c,1).(c,2)} - Consider U =…

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Q: Let X={a,b,c} and Y={1,2,3} and t={Y,0,{1,2}}. The function f={(a,1),(b,3),(c,2)}. Then the topology…

A: X = { a, b, c } , Y = { 1, 2, 3 } T = { Y, ∅,  {1, 2} } f = { (a, 1), (b, 3), (c, 3) }

Q: (1) Let X={a, b, c}, Let r-{0, X, {a}, {b}, {b, c}}. Which of the following is an open cover of X:…

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Q: If X is an inner product space and A, BC X, then AIB iff An B = {0} True O False O

A: Given that,

Q: the topology 7, = {X,ø{a},{b,c}} 1; = {Y.ø.{u}} B={X ×Y,6.{(a,u}…

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Q: Let X = {a, b, 1, 2, 3} and T = {X, p, {a}, {1,2}, {a,1,2}}. Let B = {b,3} * O B is dense in (X,T) O…

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Q: Let X be a set with more than one element. (X,t) is a topological space such tha Vxe X,{x} €T then…

A: Given a set X with more than one element.

Q: 1. If X={1,2,3,4) and T={{1,2), (3,4)} then T is 2. The collection T of all rectangular regions…

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Q: 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…

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Q: ANB +P

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Q: Consider X = {1,2,3, 4, 5} where the topology is {U C X|1 € U}. Determine whether or not X is…

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Q: disprove the following AUB s connected set then either A set prove on or B is conniedted

A: Since it is a multiple questions. As per our company guidelines, we have to solve the first one. For…

Q: Let X = {a, b, c, d} and T = { X, p, {a,b}, {c,d}}, then * An open proper subset of X may be clopen…

A: To find the true options for the given questions. Definitions: 1. Open sets can be defined as the…