论文标题
一致性对拓扑空间和图形的连通性和断开性理论的贡献的重要性
The significance of the contributions of congruences to the theory of connectednesses and disconnectednesses for topological spaces and graphs
论文作者
论文摘要
这是对最近引入的连接理论（激进类）和图形和拓扑空间的脱节性（半简单类）的一致性的调查。特别是，可以表明，可以作为Hoehnke激进分子获得连接性和断开性，并且连接性具有类似于其代数对应物的经典表征的一致性，使用自由基类别的理想。但是这种方法还表明，存在一些意想不到的差异和惊喜：拓扑空间或图形的理想herepare Hoehnke根本不必是kurosh-Amitsur激进的激进，并且在没有循环的图形类别中，没有循环，非平凡的连接性和脱节性，但所有Hoehnke Altheke Ardials Sadicals Adadicals Radicals Radicals Regentore necenerate。
This is a survey of some of the consequences of the recently introduced congruences on the theory of connectednesses (radical classes) and disconnectednesses (semisimple classes) of graphs and topological spaces. In particular, it is shown that the connectednesses and disconnectednesses can be obtained as Hoehnke radicals and a connectedness has a characterization in terms of congruences resembling the classical characterization of its algebraic counterpart using ideals for a radical class. But this approach has also shown that there are some unexpected differences and surprises: an ideal-hereditary Hoehnke radical of topological spaces or graphs need not be a Kurosh-Amitsur radical and in the category of graphs with no loops, non-trivial connectednesses and disconnectednesses exist, but all Hoehnke radicals degenerate.
