Uniformly continuous 1-1 functions on ordered fields not mapping interior to interior
Publish Year: 1387
نوع سند: مقاله ژورنالی
زبان: English
View: 367
This Paper With 7 Page And PDF Format Ready To Download
- Certificate
- من نویسنده این مقاله هستم
استخراج به نرم افزارهای پژوهشی:
شناسه ملی سند علمی:
JR_IJNAO-1-1_005
تاریخ نمایه سازی: 6 شهریور 1396
Abstract:
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.
Keywords:
Authors
Mojtaba Moniri
Department of Mathematics,Tarbiat Modarres University, Tehran
Jafar S. Eivazloo
Department of Mathematics, Tarbiat Modarres University, Tehran