nLab
subframe

A subframe is a subobject in the category Frm of frames. More explicitly, if LL is a frame, then a subframe of LL is a subset MM of the underlying set of LL such that MM is closed under arbitrary joins and finitary meets (including having the bottom and top elements).

In the correspondence between frames and locales, a subframe corresponds to a kind of quotient locale. However, only regular quotients of locales behave as quotient spaces for the purposes of topology. These correspond to regular subframes; not all subframes are regular.

Is there a convenient elementary description of when a subframe is regular?

Created on February 1, 2010 23:24:54 by Toby Bartels (173.60.119.197)