Let Q be the set of all rational .numbers a) If T= {0}U{ACQ: Q-A isfinite} prove that (Q, 7) is topological .space b) Give an example of a topology on Q which has only finite number of .elements

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 54E
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Let Q be the set of all rational
.numbers
a) If
T= {0} U{ACQ: Q-A isfinite}
prove that (Q,T) is topological
.space
b) Give an example of a topology on
Q which has only finite number of
elements
Transcribed Image Text:Let Q be the set of all rational .numbers a) If T= {0} U{ACQ: Q-A isfinite} prove that (Q,T) is topological .space b) Give an example of a topology on Q which has only finite number of elements
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