Bell, M.; Shapiro, L.; Simon, P. Products of \(\omega^*\) images. (English) Zbl 0844.54017 Proc. Am. Math. Soc. 124, No. 5, 1593-1599 (1996). Two functions \(f : X \to Y\) and \(g : X \to Z\) are called orthogonal if \(fg : X \to Y \times Z\) is a surjection. A space \(X\) is an orthogonal \(\omega^*\) image if there exists a finite-to-one surjection \(q : \omega \to \omega\) and a mapping \(f : \omega^* \to X\) such that \(f\) and \(q^*\) are orthogonal. Here \(\omega^*\) denotes the Čech-Stone remainder of the discrete space \(\omega\), and \(q^*\) denotes \(\beta q \upharpoonright \omega^*\). In this interesting paper the authors prove that all known classes of continuous images of \(\omega^*\) are in fact orthogonal \(\omega^*\) images. In addition, they prove that the product of an \(\omega ^*\) image and an orthogonal \(\omega^*\) image is an \(\omega^*\) image, and that the product of at most continuum many orthogonal \(\omega^*\) images is an orthogonal \(\omega^*\) image. Reviewer: J.van Mill (Amsterdam) Cited in 3 Documents MSC: 54D30 Compactness 54B10 Product spaces in general topology 06E05 Structure theory of Boolean algebras 54D40 Remainders in general topology Keywords:orthogonal functions; Čech-Stone remainder PDFBibTeX XMLCite \textit{M. Bell} et al., Proc. Am. Math. Soc. 124, No. 5, 1593--1599 (1996; Zbl 0844.54017) Full Text: DOI References: [1] Murray G. Bell, A first countable compact space that is not an \?* image, Topology Appl. 35 (1990), no. 2-3, 153 – 156. · Zbl 0698.54015 · doi:10.1016/0166-8641(90)90100-G [2] Aleksander Błaszczyk and Andrzej Szymański, Concerning Parovičenko’s theorem, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), no. 7-8, 311 – 314 (1981) (English, with Russian summary). · Zbl 0473.54014 [3] Eric K. van Douwen, The integers and topology, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 111 – 167. · Zbl 0561.54004 [4] Eric K. van Douwen and Teodor C. Przymusiński, Separable extensions of first countable spaces, Fund. Math. 105 (1979/80), no. 2, 147 – 158. · Zbl 0502.54037 [5] Winfried Just, The space (\?*)\(^{n}\)\(^{+}\)\textonesuperior is not always a continuous image of (\?*)\(^{n}\), Fund. Math. 132 (1989), no. 1, 59 – 72. · Zbl 0697.54002 [6] M. A. Maurice, Compact ordered spaces, Mathematical Centre Tracts, vol. 6, Mathematisch Centrum, Amsterdam, 1964. · Zbl 0134.40803 [7] Jan van Mill, An introduction to \?\?, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 503 – 567. [8] I.Parovicenko, A Universal Bicompact Of Weight \(\aleph\), Soviet Math. Doklady 4, (1963), 592-595. [9] Teodor C. Przymusiński, Perfectly normal compact spaces are continuous images of \?\?_s{\?}, Proc. Amer. Math. Soc. 86 (1982), no. 3, 541 – 544. · Zbl 0496.54020 [10] B.Sapirovski, Canonical Sets And Character. Density And Weight Of Bicompacta, Dokl. Acad. Nauk SSSR 218, (1974), 58-61. 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.