subset A ot AQuestion 4. Let A and a, be bases for topologies r, and r,, respectively,on a non-empty set X. Suppose that each Beof 8.. Show that , is coarser than 7;.& is the union of membersQuestion 5. Let S be a subbase for a topology r on X and let A be asubset of X. Show that the class S,={Ans:Ses} is a subbase for therelative topology , on A.

Since, You have asked multiple question, we will solve first question for you

Answered: Question 4. Let & and , be bases for…

Question 4. Let & and , be bases for topologies r, and , respectively, on a non-empty set X. Suppose that each Be is the union of members of 8. Show that r, is coarser than 7.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.3: Divisibility

Problem 33E

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