24. The smallest topology on R containing the collection * {(-00, a) : a e Q} is : the left ray topology the cofinite topology the indiscrete topology the usual topology the discrete topology

Q: Theorem 4.1. A space (X,T) is T¡ if and only if every point in X is a closed set.

A: Given a topological space X,T and X is a T1-space if and only if for every pair x, y of distinct…

Q: Suppose that Collection of. UA iGP is A. (CEP) set Open oppe Open. is Then S

A: We have to prove arbitrary union of open set is open.

Q: Q₂/(a) Let X=(1, 4, 5,7, 8, 9) and o= {(1,4),(4,7, 8}}, show that whether o is: (1) a subbase for a…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: (1 point) Suppose that {A, B, C'} is a partition of the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, where A…

A:

Q: Let n e N. Suppose An = {n,n +1, n +2,...} and T = {0, An}nɛN• (a) Show that T is a topology on N,…

A: As per the guideline, we are supposed to do the first three subparts of a problem. Kindly repost the…

Q: please answer all parts  thank you

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…