Keimel, Klaus; Paseka, Jan A direct proof of the Hofmann-Mislove theorem. (English) Zbl 0789.54030 Proc. Am. Math. Soc. 120, No. 1, 301-303 (1994). The theorem of the title is the assertion that, in the lattice of open subsets of a sober topological space \(X\), the filters which are Scott- open (i.e. inaccessible by directed joins) are exactly the neighbourhood filters of compact saturated subsets of \(X\). (The authors ascribe this result to a paper by K. H. Hofmann and M. W. Mislove published in 1981, although the reviewer has the impression that it had formed part of the “folklore” of the continuous-lattice community for some time before that.) The purpose of this note is to give what the authors claim to be a more direct proof of the theorem, although they freely acknowledge that the underlying idea is the same as in all previously-published proofs. Reviewer: P.T.Johnstone (Cambridge) Cited in 1 ReviewCited in 15 Documents MSC: 54D30 Compactness 06B30 Topological lattices 54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.) Keywords:Scott-open filters; lattice of open subsets; sober topological space PDFBibTeX XMLCite \textit{K. Keimel} and \textit{J. Paseka}, Proc. Am. Math. Soc. 120, No. 1, 301--303 (1994; Zbl 0789.54030) Full Text: DOI References: [1] Gerhard Gierz, Karl Heinrich Hofmann, Klaus Keimel, Jimmie D. Lawson, Michael W. Mislove, and Dana S. Scott, A compendium of continuous lattices, Springer-Verlag, Berlin-New York, 1980. · Zbl 0452.06001 [2] K. H. Hofmann and M. Mislove, Local compactness and continuous lattices, Continuous Lattices (Proceedings, Bremen, 1979) , Springer-Verlag, Berlin, 1981, pp. 209-248. [3] Steven Vickers, Topology via logic, Cambridge Tracts in Theoretical Computer Science, vol. 5, Cambridge University Press, Cambridge, 1989. · Zbl 0668.54001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.