Cartan, Henri Filters and ultrafilters. (Filtres et ultrafiltres.) (French) Zbl 0018.00302 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) Page: −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 11 Documents MSC: 54-XX General topology Citations:Zbl 0017.24305 PDF BibTeX XML Cite \textit{H. Cartan}, C. R. Acad. Sci., Paris 205, 777--779 (1937; Zbl 0018.00302) OpenURL