可连通逼近locale及其在Frm中的反射

Connectively approximable Locales and their reflections in Frm

对一个ｌｏｃａｌｅＡ，若Ａ中最大元恰可表示为一簇连通元之并，则定义Ａ为可连通逼近ｌｏｃａｌｅ．文中证明了可连通逼近ｌｏｃａｌｅ恰能表示成连通ｌｏｃａｌｅ的直积。

For a Locale A , if the largest element 1 of A can be represented by a join of some connected elements in A , then A is defined as a connectively approximable locale. It is shown that connectively approximable locales are exactly the direct product of some connected locales. From this structure theorem, it is proved that the full subcategory of Frm consisting of all connectively approximable locales is reflective.