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Products of \(\omega^*\) images. (English) Zbl 0844.54017

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.

MSC:

54D30 Compactness
54B10 Product spaces in general topology
06E05 Structure theory of Boolean algebras
54D40 Remainders in general topology
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