Filters and ultrafilters. (Filtres et ultrafiltres.) (French) Zbl 0018.00302

Cartan, Henri

C. R. Acad. Sci., Paris 205, 777-779 (1937).

This is a sequel to an earlier note on “filters” [C. R. Acad. Sci., Paris 205, 595–598 (1937; Zbl 0017.24305)]. The author characterizes compact spaces in terms of filters – a necessary and sufficient for compactness is that every “ultrafilter” be convergent. He characterizes continuous maps in terms of filters also.

Reviewer: Garrett Birkhoff (Cambridge, MA)

MSC:

54-XX

General topology

Citations:

Zbl 0017.24305