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        "quote": "直观地说，如果拓扑空间 $X$ 可以分解为两个不相交的子集 $X = A \\cup B$，且这些集合没有任何公共边界点，那么我们可以认为它是“不连通”的。由于一个集合的边界同时也是其补集的边界，这种分解能够发生的唯一方式是存在一个不同于空集或整个空间 $X$ 的集合 $A$，它完全没有边界点。由于 $b ( A ) = { \\overline { { A } } } - A ^ { o }$，$b ( A ) = \\varnothing$ 能够发生的唯一方式是 ${ \\overline { { A } } } = A ^ { o } . $ 由于 $ { \\overline { { A } } } \\subseteq A \\subseteq A ^ { o }$，集合 $A$ 必须同时等于其闭包和内部；特别地，它需要同时是开集和闭集。这引出了以下定义：如果仅有的既开又闭的子集是空集和空间 $X$ 本身，则称拓扑空间 $X$ 为 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:82292311-3a67-40cb-98ef-cfcad48c9f28\" data-concept-route=\"/concept-identities#concept-82292311-3a67-40cb-98ef-cfcad48c9f28\" id=\"first-dea27de8694dddeed0ef-zh\">连通空间(connected space)</u>。如果一个空间不是连通的，则称它为<u class=\"concept-term\" data-concept-identity=\"urn:uuid:d2b497ed-d240-4e7e-953e-13baf5792584\" data-concept-route=\"/concept-identities#concept-d2b497ed-d240-4e7e-953e-13baf5792584\" id=\"first-ab48efad4570cfb446cd-zh\">不连通空间(disconnected space)</u>。换言之，如果 $X = A \\cup B$，其中 $A$ 和 $B$ 是既开又闭的不相交集合，则 $X$ 是不连通的。如果子集 $A \\subset X$ 在相对拓扑中是连通的，则称它是连通的。",
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