Titlebook: Dimension Theory; A Selection of Theor Michael G. Charalambous Book 2019 Springer Nature Switzerland AG 2019 covering dimension.inductive d

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Wolfgang Stroebe,Klaus Jonas,Miles Hewstoneiven ., we present a Tychonoff space . which is the union of two zero subspaces .., .. such that dim...?= dim...?=?0 while dim..?=?.. We also construct Tychonoff spaces .? with dim..?=?0 that contain zero subspaces . with dim.. as large as we wish, showing the failure of the subset theorem for dim. in a strong form.

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Theorien und Modelle der Paarbeziehungany locally finite (respectively, discrete) collections.. is called . if every open cover of . has a locally finite open refinement. The proof that we give of the following fundamental result of Stone is due to Mary Ellen Rudin.

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Zum Gegenstand der Sozialpsychologie and published in full detail in Roy (Trans Am Math Soc 134:117–132, 1968), is generally considered to be of forbidding complexity. In this chapter we present Kulesza’s much simpler metrizable space . with . and ., published in his paper Kulesza (Topol Appl 35:109–120, 1990) of 1990.

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Book 2019e emphasis on the negative results for more general spaces, presenting a readable account of numerous counterexamples to well-known conjectures that have not been discussed in existing books. Moreover, it includes three new general methods for constructing spaces: Mrowka‘s psi-spaces, van Douwen‘s t

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The Dimension of Euclidean Spaces, to Morita and Smirnov, who generalized the result of Alexandroff for the case of compact Hausdorff spaces. From this inequality, the countable sum theorem for . and the Urysohn inequality for ., it will follow that . and ..

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Connected Components and Dimension,∈?., is the union of all connected subspaces of . that contain .. The intersection of all clopen sets of . that contain ., denoted here by ., is called the . of .. If . for every .?∈?., . is called .. If . for every .?∈?., . is called .. Note that both . and . are closed subsets of . and . is connected.

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Universal Spaces for Separable Metric Spaces of Dimension at Most ,,. space ., which consists of all points of . that have at most . rational coordinates, is a universal space for the class of all separable metric spaces of covering dimension at most .. We first need some preliminary results.

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