A topology $au$ on a set $X$ is called maximal connected if it isconnected, but no strictly finer topology $au^* > au$ is connected. Weconsider a construction of so-called tree sums of topological spaces, and weshow how this construction preserves maximal connectedness and also relatedproperties of strong connectedness and essential connectedness. We also recall the characterization of finitely generated maximal connectedspaces and reformulate it in the language of specialization preorder andgraphs, from which it is imminent that finitely generated maximal connectedspaces are precisely $T_rac{1}{2}$ tree sums of copies of the Sierpi'nskispace.
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机译:拓扑$ tau $ oon a set $ x $ card maximal连接如果它是连接的,但没有严格更精细的拓扑$ tau ^ *> tau $。 WECONSIDER建立了所谓的拓扑空间的树和,以及WELESWORCHIAL如何保留最大关联,以及强大的连通性和基本关联的相关性。我们还回顾了有限生成的最大连接空间的特征,并以专业化预购和图表的语言重新格式化,从中迫切地生成的最大连接空间恰好$ t_ frac {1} {2} $树和副本的副本sierpi 'nskispace。
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