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Uniformly Continuous 1-1 Functions on Ordered Fields Not Mapping Interior To Interior
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نویسنده
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Moniri Mojtaba ,Eivazloo Jafar S.
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منبع
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Iranian Journal Of Numerical Analysis And Optimization - 2008 - دوره : 1 - شماره : 1 - صفحه:59 -65
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چکیده
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In an earlier work we showed that for ordered fields f not isomorphic tothe reals r, there are continuous 1-1 functions 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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کلیدواژه
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Ordered Field ,Gap ,Monotone Complete ,Open Map
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آدرس
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Tarbiat Modares University, Department Of Mathematics, ایران, Tarbiat Modares University, Department Of Mathematics, ایران
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پست الکترونیکی
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mojmon@ipm.ir
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Authors
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