Let X be the graph of f(x) = x-1s given below

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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1. Let X be the graph of f(x) = x2/3 given below
%3D
that is, X is the subset of R x R satisfying the given equation.
Declare that a subset A of X is basic if
A = Xn B,((x, y))
for some open ball B.((x, y)) = {(a, b) e R × R| /(x – a)² + (y – b)² < c}.
Let Aj and A2 be basic subsets of X.
i. Is Aj U A2 a basic subset of X? Prove or provide a counterexample.
ii. Is A1 N A2 a basic subset of X? Prove or provide a counterexample.
Transcribed Image Text:1. Let X be the graph of f(x) = x2/3 given below %3D that is, X is the subset of R x R satisfying the given equation. Declare that a subset A of X is basic if A = Xn B,((x, y)) for some open ball B.((x, y)) = {(a, b) e R × R| /(x – a)² + (y – b)² < c}. Let Aj and A2 be basic subsets of X. i. Is Aj U A2 a basic subset of X? Prove or provide a counterexample. ii. Is A1 N A2 a basic subset of X? Prove or provide a counterexample.
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