论文标题
在$ \ mathbb {r}^2 $中连接集的算术总和
On arithmetic sums of connected sets in $\mathbb{R}^2$
论文作者
论文摘要
我们证明，对于两个连接的集合，$ e，f \ subset \ mathbb {r}^2 $，红衣主义大于$ 1 $，如果$ e $和$ f $的一个是紧凑而不是线段，则算术和$ e+e+f $具有非空的内部装置。这改善了Banakh，Jabłońska和Jabłoński[4，定理4]在尺寸二的结果，这是他们放松他们假设$ E $和$ f $都紧凑的。
We prove that for two connected sets $E,F\subset\mathbb{R}^2$ with cardinalities greater than $1$, if one of $E$ and $F$ is compact and not a line segment, then the arithmetic sum $E+F$ has non-empty interior. This improves a recent result of Banakh, Jabłońska and Jabłoński [4,Theorem 4] in dimension two by relaxing their assumption that $E$ and $F$ are both compact.
