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}, {1,2,3}, {4,5,6}, {2,4,5,6}} T1 is not a topology and T2 is a topology on O T1 and T2 are both topologies on X O T1 and T2 are both not topologies on T1 is a topology on X and T2 is not a topology on X

Q: Let X = (a, b, c, d) and TX = (Ø, X, (b), {b.c), {a,b,d}) be a topology 3, 4) and TY = (0, Y, (3),…

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 T be the Euclidean topology. Let A = [0,2] and B = [0,1[, then B is clopen in (A, TA) where TA…

A:

Q: Q1:A) Let X = R and r be the usual topology on R.If Y-[4,6). 1) Determine the open ,closed ,open and…

A: Given that, X=Rand τ is usual topology on R Given that Y=[4,6). 1) 4,5 Is open in the given topology…

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, Tx) and (Y, Ty) be two topological spaces, such that X = {a, b,c, d}, Tx = {6, X, {a}, {a,…

A: I

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).…

A:

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: Let T be the Euclidean topology. Let A = [0,1] and B =]0.5,1] then B is clopen in (A,T) where T is…

A: YOUR ANSWER IS True.

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

A:

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…

A:

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),…

A:

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: - 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: Let X = {a, b, c, d} and TX = {0, X, {b}, (b,c), {a,b.d}} be a topology on X. Let Y ={1, 2, 3, 4}…

A: A function is continuous if and only if inverse image of every open set is open

Q: E.X; Let T = {E₁ = (-∞,a): a = R}U{R,Ø} be a topology on R and let A = [2,3), B=(3,4), C = (1,5], D…

A: It is given that,  T = Ea=-∞, a : a∈ℝ∪ℝ, ∅ is a topology on ℝ. We have to find the closure of the…

Q: Let S be the subset of the ℝ2 given by all pairs (x, y) so that x2 + y2 = 2. Show that S is a closed…

A:

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 T={X, {a}, {a,b).{a,c,d}, {a,b,c,d}, {a,b,c}} be a topology on X=(a,b,c,d,e). (ii) Find N.…

A: Given : (X, T) be a topological space,  where  X = {a, b, c, d, e} and T = {X, ϕ, {a}, {a, b}, {a,…

Q: Let X = {a, b, c, d} and TX = {ø, X, {b}, {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3, 4}…

A:

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: Let X = {a, b, c, d} and TX = {Ø, X, {b}, {b,c), {a,b,d}} be a topology on X. Let Y = {1, 2, 3, 4}…

A: A map is continuous if and only if inverse image of every open set is open

Q: Let (X, T) topological space, where X = {a,b,c,d} and T = {X. Ø, {a}, {a,b}, {a,b,c}} Find a) Basic…

A: Given that X, T topological space, where X=a, b, c, d and T=X, ϕ, a, a, b, a, b, c.

Q: Let X = {a, b, c, d} and TX = {Ø, X, {b}, {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3, 4}…

A:

Q: Let X = {a,b,c,d} and Tx = {X, Ø, {a}, {a, b}, {a,b,c}} be a topology on X. Let y = {1,2,3,4} and Ty…

A: I have used the definition of continuous function in topological space.

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 = {0, p, q, r, s} and consider the topology on X below: T = {X,0, {o}, {q,r}, {o,q, r}, {p, q,…

A:

Q: Let X = {a, b, c, d} and TX = {ø, X, {b}, %3D {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3,…

A: A function is continuous if and only if inverse image of every open set is open

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: 18: Consider the two linear maps T, and T2 on V, defined as T(X, X, x) = (0, xz x) and T,(x , x, x)…

A:

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…

A:

Q: Let X= (a, b, c, d) and TX = {Ø, X, {b}, {b,c}, {a,b,d}} be a topology on X. Let Y= 3, 4) and TY=…

A: A function is continuous if and only if inverse image of every open set is open

Q: Let X = {a, b, c, d} and TX = {ø, X, {b}, {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3, 4}…

A:

Q: Let X = {1, 2, 3, 4, 5, 6}. Prove that in general, if X is finite there is only one topology for X…

A: Let X = {1, 2, 3, 4, 5, 6}. Prove that in general, if X is finite there is only one topology for X…

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

A:

Q: 10. Let (X, Tx) and (Y, Tr) be two topological spaces, such that X = {a, b,c, d}, Tx = {ó, X, {a},…

A:

Q: 2. Consider the topology 7, = {X,ø,{a},{b,c}}_on X = {a,b,c} and 1, = {Y,ø.{u}} Y = {u,v} . the…

A:

Q: Let X = {a, b, c, d} and TX = {Ø, X, {b}, {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3, 4}…

A:

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

A:

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},…

A:

Q: Let A = {2, 4} and B = {1, 3, 5} and define rela- tions U, V, and W from A to B as follows: For…

A: (a) First obtain the 3 relations as follows.

Q: Let X = {a, b, c, d} and TX = {ø, X, {b}, {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3, 4}…

A:

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: prove that each of the following sets of points is collinear 1. A(4,5), B(3,3), C(1,-1) 2.…

A: As per guidelines, we are supposed to solve only first question. Please repost other questions…

Q: Let (X, Tx) and (Y, Ty) be two topological spaces, such that X = {a, b, c, d}, Tx = {ø, X, {a}, {a,…

A: We need to check the necessary and sufficient conditions for continuity

Q: Let X = {1, 2, 3, 4} and T be the discrete topology on X. Consider the following statements: (a)…

A: When T is the discrete topology of X, then it means Topology of T on X is the collection of all…

Q: Let X = {a, b, c, d} and TX = {ø, X, {b}, {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3, 4}…

A:

Q: Suppose di and d2 are metrics on a set S. Suppose di generates the topology T1 = {A, Ø, S, B} and d2…

A: We are given that d1 and d2 are metrics on a set S. Further, d1 generates the topology τ1=A,φ,S,B…