论文标题
嘴唇集的表征
Characterization of lip sets
论文作者
论文摘要
我们用$ {\ Mathbb r} \ to {{\ Mathbb r}} $ by $ {\ Mathrm {lip}} f $。在函数$ f的函数$ f：{\ mathbb r} \ to {{\ mathbb r}} $中表示本地的``小'lipschitz常数''表示本地``小lipschitz''表示本地的``小lipschitz''来表示本地``\ {\ mathrm {lip}} f $。在本文中解决以下问题： $ f $使$ {\ mathrm {lip}} f = \ mathbf {1} _e $？ 在较早的论文中，我们介绍了强烈的单面密集集的概念。我们的主要结果是$ {\ mathrm {lip}} 1 $设置为闭合集合的可数工会，它们是强烈的单向密集的。 我们还表明，更强有力的语句不是正确的，即有强烈的单面密集$ f_σ$集，而不是$ {\ mathrm {lip}} 1 $。
We denote the local ``little" Lipschitz constant of a function $f: {\mathbb R}\to { {\mathbb R}}$ by $ {\mathrm{lip}}f$. In this paper we settle the following question: For which sets $E {\subset} { {\mathbb R}}$ is it possible to find a continuous function $f$ such that $ {\mathrm{lip}}f=\mathbf{1} _E$? In an earlier paper we introduced the concept of strongly one-sided dense sets. Our main result characterizes $ {\mathrm{lip}}1$ sets as countable unions of closed sets which are strongly one-sided dense. We also show that a stronger statement is not true i.e. there are strongly one-sided dense $F _σ$ sets which are not $ {\mathrm{lip}}1$.
