Bell, Murray Polyadic spaces of countable tightness. (English) Zbl 1008.54015 Topology Appl. 123, No. 3, 401-407 (2002). Summary: We answer a question of J. Gerlits [Stud. Sci. Math. Hung. 13, 1-17 (1978; Zbl 0475.54012)] by constructing a polyadic space of countable tightness which is not a continuous image of \(A_{\kappa}^{\omega}\) (\(A_{\kappa}\) is the one point compactification of the discrete space \(\kappa\)). The space is a uniform Eberlein compact space of weight \(\omega _1\). It follows that being an \(A_{\kappa}^{\omega}\) image is not preserved by countable inverse limits. Cited in 2 Documents MSC: 54D30 Compactness 54B10 Product spaces in general topology 06E15 Stone spaces (Boolean spaces) and related structures 54B15 Quotient spaces, decompositions in general topology 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) Keywords:uniform Eberlein compact; boolean; countable tightness Citations:Zbl 0475.54012 PDFBibTeX XMLCite \textit{M. Bell}, Topology Appl. 123, No. 3, 401--407 (2002; Zbl 1008.54015) Full Text: DOI References: [1] Bell, M., A Ramsey theorem for polyadic spaces, Fund. Math., 150, 189-195 (1996) · Zbl 0890.54020 [2] Bell, M., Universal uniform Eberlein compact spaces, Proc. Amer. Math. Soc., 128, 2191-2197 (2000) · Zbl 0949.54023 [3] M. Bell, Tightness in polyadic spaces, Topology Proc., to appear; M. Bell, Tightness in polyadic spaces, Topology Proc., to appear [4] Benyamini, Y.; Starbird, T., Embedding weakly compact sets into Hilbert space, Israel J. Math., 23, 137-141 (1976) · Zbl 0325.46023 [5] Benyamini, Y.; Rudin, M. E.; Wage, M., Continuous images of weakly compact subsets of Banach spaces pacific, J. Math., 70, 309-324 (1977) · Zbl 0374.46011 [6] Gerlits, J., On a generalization of dyadicity, Studia Sci. Math. Hung., 13, 1-17 (1978) · Zbl 0475.54012 [7] Koppelberg, S., General theory of Boolean algebras, (Monk, J.; Bonnet, R., Handbook of Boolean Algebras, Vol. 1 (1989), North-Holland: North-Holland Amsterdam) [8] Mrowka, S., Mazur theorem and \(m\)-adic spaces, Bull. Acad. Pol. Sci., 18, 6, 299-305 (1970) · Zbl 0194.54302 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.