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8. Let X be a set and ß be a basis for a topology T on X. Then T equals the collection of all unions of elements of ß. Prove this statement and give an example to validate your proof.

8. Let X be a set and ß be a basis for a topology T on X. Then T equals the collection of all unions of elements of ß. Prove this statement and give an example to validate your proof.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 30E: Let be as described in the proof of Theorem. Give a specific example of a positive element of .
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8. Let X be a set and B be a basis for a topology T on X. Then T equals the collection of all unions of elements of B . Prove this statement and give an example to validate your proof.
Transcribed Image Text:8. Let X be a set and B be a basis for a topology T on X. Then T equals the collection of all unions of elements of B . Prove this statement and give an example to validate your proof.
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