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 ]0,1[ R is homeomorphic to ]0, +¤[ 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 ]0,1[ R is homeomorphic to ]0, +¤[ O 1-0,0] is homeomorphic to [0,+∞[

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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