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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The Countable Sum Theorem for Covering Dimension,In this chapter we prove two of the most important results for covering dimension, the countable sum theorem for normal spaces and the subset theorem for perfectly normal spaces. Both results are due to ?ech.

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Coincidence, Product and Decomposition Theorems for Separable Metric Spaces,Let ., . be disjoint closed sets of a non-empty compact regular space . with .. Let . be a finite open cover of .. Then there are disjoint closed sets .., .. of . such that . and the trace of . on .???(..?∪?..) has a finite open refinement . of order at most .???1.

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Axiomatic Characterization of the Dimension of Separable Metric Spaces,Consider the following axioms for a dimension function . on a class of spaces . that contains all Euclidean cubes . and every space that is homeomorphic to a subspace of a member of .. Bear in mind that by our definition of a dimension function, . if . and .? are homeomorphic, and . iff .?=??.

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Cozero Sets and Covering Dimension dim0,In this chapter we establish the fundamental properties of the dimension function dim. that was defined earlier in Chap. ., including the countable sum theorem and the subset theorem. We first recall some standard properties of zero and cozero sets.

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Dimension Theory978-3-030-22232-1Series ISSN 1875-7634 Series E-ISSN 2215-1885

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Jacques-Philippe Leyens,Benoit Dardenne 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 ..