论文标题
在收敛晶格和收敛空间清醒的点上
On points of convergence lattices and sobriety for convergence spaces
论文作者
论文摘要
我们表征了收敛空间$（x，ξ）$，使得$（\ mathbb {p} x，\lim_ξ）$的点空间在收敛晶格类别中为$（x，ξ）$。在途中，我们在收敛空间中研究清醒和公理$ t_ {d} $的变体。离开拓扑空间领域时出现了新现象。我们获得了融合晶格的点空间的新事后，并研究了它的特殊商，在拓扑空间$（x，ξ）$的情况下，在$ l =（\ mathbb {p} x，\lim_ξ）$中，证明对$ x $ $ x $的sobration so hist so hinds $ x $ $ x $。
We characterize the convergence spaces $(X,ξ)$ such that the space of points of $(\mathbb{P}X,\lim_ξ)$ in the category of convergence lattices is $(X,ξ)$. On the way, we study variants of sobriety and of the axiom $T_{D}$ in convergence spaces. New phenomena appear when leaving the realm of topological spaces. We obtain new hindsight into the space of points of a convergence lattice and study a special quotient of it, which, in the case $L=(\mathbb{P}X,\lim_ξ)$ for a topological space $(X,ξ)$, turns out to be homeomorphic to the sobrification of $X$.
