6) Let p and q be two points in a set, X. Consider the two collections of subsets of X: I. = {Ø, X, U|p E U and q E U} J = {Ø, 2 X, U|p E U orq E U} (i) Prove that T is a topology on X or show that it is not. 1 (ii) Prove that Tis a topology on X or show that it is not. 2

Q: 1. Let X = {a,b,c} and B={{a,c}.{b,c}}cP(X). Show that B cannot be a base for any topology r on X.

A: According to the answering guidelines, we shall solve first question only. If you want others to be…

Q: udg Exercise: If X = {a,b,c,d,e} Determine whether or not each of the following collections of…

A:

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

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Let T be the finite closed topology on a finite set X, then * O Tis the Euclidean topology O Tis the…

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

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: Show that there is no topology on X={a,b,c,d,e} based on the family B={{a,b},{a,b,d},{b,d,e}}

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Q: m) Show that if T;,T; and Ty are topologies on a set X.then r, nnt, is a topology on X.

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

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: 4. Let X be any set and 7 be the countable complement topology on X. b) If X is uncountable, then…

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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: 5. Let X be a set and p E X. b) If 72 = {A C X : p ¢ A}U{X}is a topology on X, then determine…

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Q: Let (X, sx) (Y, sy) be two partially ordered sets. se+ Xx Y is defined as The relation son the (a,…

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Q: Q1.Consider X ={a,b, c, d, f, g} .Let T={ó, X, {a,b, c} ,{g};{a,b, c, g}} (a) Prove that T is a…

A: Since you post a question with multy part, we solve only first three, if you need any particular…

Q: 3. Let X = {a,b,c ,d, e}, f ={{a,b}.{b.c}.fc.e}.fe}}cP(X) Find the topology z on X generated by B.

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Q: 2. Let X = {a,b,c,d} and T = {ø,{a},{b},{a,b},{a,b,d},{a,b,c}, X}. a) Show that T is a topology on…

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Q: Consider the topology T on X= (a, b, c, d, e), (X, Ø, (a), (e,d}, {a, e, d), (b, c, d, e}} Show that…

A: It is given that,  X = {a, b, c, d, e} and  T = X, ∅, a, c, d, a, c, d, b, c, d, e be a topology on…

Q: Show that the collection of all sets which are union of sets of the form [a, b) is a topology on R.

A: To Show: The collection of all sets which are the union of sets of the form [a, b) is a topology on…

Q: c) Let u be a usual topology on a set of real numbers R, and E= {2,3,6 Show that whether E is…

A: Given that R is endowed with the usual topology and that E={2,3,6}. We shall state a definition and…

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

A:

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

A: Connected Space: A space can be separated if it can be broken up into two disjoint open sets. Let X…

Q: 4. Let R be endowed with its standard topology. a) Find the closures of : i. Q ii. R-Q iii.…

A: This is a problem of topology.

Q: Q2. Answer as true or false: (a) f-'((AUB)nC) = (ƒ-'(A)n f-1C)) U (f-1(B) n f-1(C)). (b) Given the…

A: (a) is True. (b) is False.

Q: Arrange the choices in order 1,2,3.. to prove: For any sets A, B and C Ax (BUC) = (A x B) U (A x C),…

A: SOLUTION-

Q: Show that if a topological space has a finite number of points each of which is closed then it has…

A: Topology question.

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: 3) let X be discrete topology and Ac X, find A ?

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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: