Uniformly continuous 1-1 functions on ordered fields not mapping interior to interior
سال انتشار: 1387
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 345
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شناسه ملی سند علمی:
JR_IJNAO-1-1_005
تاریخ نمایه سازی: 6 شهریور 1396
چکیده مقاله:
In an earlier work we showed that for ordered fields F not isomorphic to the reals R, there are continuous 1-1 unctions on [0, 1]F which map some interior point to a boundary point of the image (and so are not open). Here we show that over closed bounded intervals in the rationals Q as well as in all non-Archimedean ordered fields of countable cofinality, there are uniformly continuous 1-1 functions not mapping interior to interior. In particular, the minimal non-Archimedean ordered field Q(x), as well as ordered Laurent series fields with coefficients in an ordered field accommodate such pathological functions.
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نویسندگان
Mojtaba Moniri
Department of Mathematics,Tarbiat Modarres University, Tehran
Jafar S. Eivazloo
Department of Mathematics, Tarbiat Modarres University, Tehran