论文标题
欧几里得空间中的定向和不可逆转的路径
Directed and irreversible path in Euclidean spaces
论文作者
论文摘要
这个简短说明的目的是将$ {\ stackrel {\ rm \ longrightArrow} {\ rm \ mathbb {rm \ mathbb {rm}^n}} $与$ {\ stackrel {\ stackrel {\ rm ir ir}的不可逆转路径联系起来，将定向路径相关联。我们首先表明，有一个有向路径从$ x $到$ {\ stackrel {\ rm \ rm \ longrightArrow} {\ rm \ rm \ rm \ mathbb {r}^n}} $ iff，存在$ {\ stackrel {\ rm ir irmir { \ mathbb {r}^n}} $。另外，我们证明，$ {\ stackrel {\ rm \ longrightArrow} {\ rm \ mathbb {rm \ mathbb {r}^n}} $是$ {\ stackrel {\ rm ir} {\ rm ir} {\ rm \ rm \ rm \ mathbb {rm mathbb {rm mathbb {rm mathbb {rm mathbb {rm mathbb {r} =
The aim of this very short note is to relate the directed paths in ${\stackrel{\rm \longrightarrow}{\rm \mathbb{R}^n}}$ to the irreversible paths in ${\stackrel{\rm ir}{\rm \mathbb{R}^n}}$. We first show that there is a directed path from $x$ to $y$ in ${\stackrel{\rm \longrightarrow}{\rm \mathbb{R}^n}}$ iff there exists an irreversible path with same initial and terminal points in ${\stackrel{\rm ir}{\rm \mathbb{R}^n}}$. Also, we prove that every directed path in ${\stackrel{\rm \longrightarrow}{\rm \mathbb{R}^n}}$ is an irreversible path in ${\stackrel{\rm ir}{\rm \mathbb{R}^n}}$.
