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A large plane set intersecting lines in infinitely many directions in at most one point
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-01-22 , DOI: 10.1090/proc/15341 Vladimir Eiderman , Michael Larsen
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-01-22 , DOI: 10.1090/proc/15341 Vladimir Eiderman , Michael Larsen
Abstract:We prove that for every at most countable family 
of real functions on 
there is a single-valued real function 
, 
, such that the Hausdorff dimension of the graph 
of 
equals 2, and for every 
and every 
, the intersection of 
with the graph of the function 
consists of at most one point. We also construct a family of functions of cardinality continuum and a function 
with similar properties.
中文翻译：
大型平面最多在一个点上以无限多个方向设置相交线
摘要：证明了对每一个至多可数的家庭的实际功能上有一个单值实函数，例如该图形的维数的等于2，并为每一位，相交，并且在图表该功能最多包含一个点。我们还构造了一个基数连续函数和具有相似属性的函数。
更新日期：2021-02-08
of real functions on there is a single-valued real function , , such that the Hausdorff dimension of the graph of equals 2, and for every and every , the intersection of with the graph of the function consists of at most one point. We also construct a family of functions of cardinality continuum and a function with similar properties. 中文翻译：
大型平面最多在一个点上以无限多个方向设置相交线
摘要：证明了对每一个至多可数的家庭的实际功能上有一个单值实函数，例如该图形的维数的等于2，并为每一位，相交，并且在图表该功能最多包含一个点。我们还构造了一个基数连续函数和具有相似属性的函数。
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