A property Is said to be a topological property if it is preserved by homeomorphism. Suppose that R is equipped with the usual topology, then the boundedness and the closedness are not topological properties because O [0,1] is not homeomorphic to ]0,1[ Ris homeomorphic to ]0, +o[ Ris homeomorphic to ]0,1[ O 1-0,0] is homeomorphic to [0,+[
A property Is said to be a topological property if it is preserved by homeomorphism. Suppose that R is equipped with the usual topology, then the boundedness and the closedness are not topological properties because O [0,1] is not homeomorphic to ]0,1[ Ris homeomorphic to ]0, +o[ Ris homeomorphic to ]0,1[ O 1-0,0] is homeomorphic to [0,+[
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 1E: Complete the proof of Theorem 5.30 by providing the following statements, where and are arbitrary...
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