A meet in a frame is exact if it join-distributes with every element, it is strongly exact if it is preserved by every frame homomorphism. Hence, finite meets are (strongly) exact which leads to the concept of an exact resp. strongly exact filter, a filter closed under exact resp. strongly exact meets. It is known that the exact filters constitute a frame $${\mathrm{Filt}}_{{\textsf {E}}}(L)$$ somewhat surprisingly isomorphic to the frame of joins of closed sublocales. In this paper we present a characteristic of the coframe of meets of open sublocales as the dual to the frame of strongly exact filters $${\mathrm{Filt}}_{{\textsf {sE}}}(L)$$ .

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精确和强精确过滤器

如果帧中的相遇与每个元素连接分布，则它是精确的，如果它被每个帧同态保留，则它是强精确的。因此，有限满足是（强）精确的，这导致了精确响应的概念。强精确过滤器，在精确响应下关闭的过滤器。强烈精确满足。众所周知，精确的过滤器构成了一个框架 $${\mathrm{Filt}}_{{\textsf {E}}}(L)$$ 有点令人惊讶地与封闭子区域的连接框架同构。在本文中，我们将开放子区域的汇合共框的特征呈现为强精确过滤器 $${\mathrm{Filt}}_{{\textsf {sE}}}(L)$$ 框架的对偶。