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Polyadic spaces of countable tightness. (English) Zbl 1008.54015

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.

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)

Citations:

Zbl 0475.54012
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References:

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