query: The union of a finite sequence of connected sets that meet pairwise is connected
positive_passages.docid: 18572
positive_passages.text: Union of a family of connected pairwise not disjoint subspaces is connected
negative_passages.docid: 95244
negative_passages.text: Prove that a finite union of closed sets is also closed
negative_passages.docid: 59289
negative_passages.text: Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
negative_passages.docid: 3404
negative_passages.text: What are the convergent sequences in the cofinite topology
negative_passages.docid: 115695
negative_passages.text: If $X$ is a connected subset of a connected space $M$ then the complement of a component of $M \setminus X$ is connected
negative_passages.docid: 100437
negative_passages.text: Classification of connected subsets of the real line (up to homeomorphism)
negative_passages.docid: 2575
negative_passages.text: Showing that $\mathbb{R}$ is connected
negative_passages.docid: 103769
negative_passages.text: The Cartesian product of a finite number of countable sets is countable
negative_passages.docid: 67279
negative_passages.text: Is the union of finitely many open sets in an omega-cover contained within some member of the cover?
negative_passages.docid: 31266
negative_passages.text: Proof of "the continuous image of a connected set is connected"
negative_passages.docid: 89506
negative_passages.text: Union of disjoint sets : Equivalence relations
negative_passages.docid: 106455
negative_passages.text: intersection of infinite collection of finite sets?
negative_passages.docid: 112731
negative_passages.text: If $Y$ is connected, why is $A\cup Y$ connected in this case?
negative_passages.docid: 108052
negative_passages.text: Does any connected metrizable space with more than one element have uncountably many open sets, each generating a connected subspace?
negative_passages.docid: 30079
negative_passages.text: Is for open connected $U$ the set $U_\varepsilon$ for small $\varepsilon$ connected?
negative_passages.docid: 36044
negative_passages.text: Show $\Bbb R ^n$ with a finite set removed is still connected.
negative_passages.docid: 16654
negative_passages.text: Unions and Intersections of Open Sets are Open