论文标题
拓扑类型的空间类型，包括在本地紧凑的可迁移空间上的某些指标，并具有紧凑的拓扑结构
The topological type of spaces consisting of certain metrics on locally compact metrizable spaces with the compact-open topology
论文作者
论文摘要
对于可分离的本地紧凑而不是紧凑的Metrizable Space $ x $，让$αx= x \ cup \ {x_ \ infty \} $是Infinity $ x_ \ infty $的点的单点压实。我们用$ em（x）$表示由$ x $上的可接受指标组成的空间，可以将其扩展到$αx$上的可允许的指标，并具有紧凑型拓扑。令$ \ mathbf {c} _0 \ subset（0,1）^\ mathbb {n} $为序列的空间，融合到$ 0 $。在本文中，我们将证明，如果$ x $可分开，本地连接且本地紧凑但不紧凑，并且存在$ x $连接的semence $ \ {c_i \} $，以便所有正整数$ i，j \ in \ mathbb {n} $ with $ | i- j | \ leq 1 $，$ c_i \ cap c_j \ neq \ neq \ emptyset $，对于每个紧凑型套装$ k \ subset x $，有一个正整数$ i（k）\ in \ mathbb {n} $，因此对于任何$ i \ geq i \ geq i（k）$，$ c_i \ c_i \ set $ em（$） \ Mathbf {C} _0 $。
For a separable locally compact but not compact metrizable space $X$, let $αX = X \cup \{x_\infty\}$ be the one-point compactification with the point at infinity $x_\infty$. We denote by $EM(X)$ the space consisting of admissible metrics on $X$, which can be extended to an admissible metric on $αX$, endowed with the compact-open topology. Let $ \mathbf{c}_0 \subset (0,1)^\mathbb{N}$ be the space of sequences converging to $0$. In this paper, we shall show that if $X$ is separable, locally connected and locally compact but not compact, and there exists a sequence $\{C_i\}$ of connected sets in $X$ such that for all positive integers $i, j \in \mathbb{N}$ with $|i - j| \leq 1$, $C_i \cap C_j \neq \emptyset$, and for each compact set $K \subset X$, there is a positive integer $i(K) \in \mathbb{N}$ such that for any $i \geq i(K)$, $C_i \subset X \setminus K$, then $EM(X)$ is homeomorphic to $ \mathbf{c}_0$.
