Uniform isomorphism




In the mathematical field of topology a uniform isomorphism or uniform homeomorphism is a special isomorphism between uniform spaces which respects uniform properties.




Contents






  • 1 Definition


  • 2 Examples


  • 3 See also


  • 4 References





Definition


A function f between two uniform spaces X and Y is called a uniform isomorphism if it satisfies the following properties




  • f is a bijection


  • f is uniformly continuous

  • the inverse function f-1 is uniformly continuous


If a uniform isomorphism exists between two uniform spaces they are called uniformly isomorphic or uniformly equivalent.



Examples


The uniform structures induced by equivalent norms on a vector space are uniformly isomorphic.



See also




  • homeomorphism is an isomorphism between topological spaces


  • isometric isomorphism is an isomorphism between metric spaces



References



  • John L. Kelley, General topology, van Nostrand, 1955. P.181.







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