极大连通空间的树和
Tree sums of maximal connected spaces
摘要：
集合$X$上的拓扑$τ$称为极大连通，如果它是连通的，但没有严格更细的拓扑$τ^* > τ$是连通的。我们考虑一个所谓的树和拓扑空间的建设，我们展示了如何建设保持最大连通性和强连通性和本质连通性的相关性质。我们还回顾了Sierpienski生成的极大连通空间的特征，并将其用特殊化预序和图的语言重新表述，从中可以清楚地看出，Sierpienski生成的极大连通空间正是Sierpienski空间的副本的$T_\frac{1}{2}$树和。
英文摘要：
A topology $τ$ on a set $X$ is called maximal connected if it is connected, but no strictly finer topology $τ^* > τ$ is connected. We consider a construction of so-called tree sums of topological spaces, and we show how this construction preserves maximal connectedness and also related properties of strong connectedness and essential connectedness. We also recall the characterization of finitely generated maximal connected spaces and reformulate it in the language of specialization preorder and graphs, from which it is clear that finitely generated maximal connected spaces are precisely $T_\frac{1}{2}$ tree sums of copies of the Sierpiński space.
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