第一可数空间 First-countable space

（重定向自First Axiom of Countability）

在拓扑学上，第一可数空间（First-countable space）是指有可数的局部基的拓扑空间，即对于 $x \in X$ ，存在 $x$ 的开邻域串行 $U_1,U_2,U_3,...$ ，使得对于任意的邻域 $V$ ，存在整数 $i$ 使得 $U_i \subseteq V$ 。

单词	First Axiom of Countability
释义	First Axiom of Countability 中文百科第一可数空间 First-countable space （重定向自First Axiom of Countability）在拓扑学上，第一可数空间（First-countable space）是指有可数的局部基的拓扑空间，即对于 $x \in X$ ，存在 $x$ 的开邻域串行 $U_1,U_2,U_3,...$ ，使得对于任意的邻域 $V$ ，存在整数 $i$ 使得 $U_i \subseteq V$ 。英语百科 First-countable space 第一可数空间（重定向自First Axiom of Countability） In topology, a branch of mathematics, a first-countable space is a topological space satisfying the "first axiom of countability". Specifically, a space X is said to be first-countable if each point has a countable neighbourhood basis (local base). That is, for each point x in X there exists a sequence N₁, N₂, … of neighbourhoods of x such that for any neighbourhood N of x there exists an integer i with N_i contained in N. Since every neighborhood of any point contains an open neighborhood of that point the neighbourhood basis can be chosen without loss of generality to consist of open neighborhoods.
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First Axiom of Countability

第一可数空间 First-countable space

First-countable space 第一可数空间