[Cross post from Math overflow.] Let X be a locale. Then there is the Vietoris locale construction, V, introduced by Johnstone (it's in Stone Spaces, but see also the 1985 paper, 'Vietoris Locales and Localic Semilattices'). The functor V:Loc→Loc is something like taking the locale of all finite sublocales; e.g., if X is discrete then the points of V(X) are the finite subsets of X. In his 1985 paper Johnstone alludes to the fact that if X is compact then so is V(X). But the proof, which is not explicit in the paper, uses a transfinite induction. I believe there is a much simpler proof, but have not found any references to this in the literature. Does anyone know about this specific result being published in the last 25 years? Thanks, Christopher Leonardo UK Ltd Registered Office: 1 Eagle Place, St James’s, London SW1Y 6AF A company registered in England & Wales. Company no. 02426132 ******************************************************************** This email and any attachments are confidential to the intended recipient and may also be privileged. If you are not the intended recipient please delete it from your system and notify the sender. You should not copy it or use it for any purpose nor disclose or distribute its contents to any other person. ******************************************************************** You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=files&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=leave&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>