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

A:

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: topological space a

A: Presumably, the closure of Q in R under the usual topology. It suffices to show that for every real…

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.

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: 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…

A: