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 Rishomeomorphic to ]a,b[ R is homeomorphic to ]-∞, O[ R is homeomorphic to ] -«, 0] O Na,b] is not homeomorphic to Ja,b[

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 Rishomeomorphic to ]a,b[ R is homeomorphic to ]-∞, O[ R is homeomorphic to ] -«, 0] O Na,b] is not homeomorphic to Ja,b[

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.5: Permutations And Inverses

Problem 8E: 8. a. Prove that the set of all onto mappings from to is closed under composition of mappings. b....

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