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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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发表于 2025-3-21 16:16:14 | 显示全部楼层 |阅读模式
书目名称Dimension Theory
副标题A Selection of Theor
编辑Michael G. Charalambous
视频video
概述Presupposed topological definitions and facts are carefully recalled.Includes numerous exercises proving presupposed facts.Includes numerous exercises of further interest.Helpful hints accompany exerc
丛书名称Atlantis Studies in Mathematics
图书封面Titlebook: Dimension Theory; A Selection of Theor Michael G. Charalambous Book 2019 Springer Nature Switzerland AG 2019 covering dimension.inductive d
描述This book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case. Its distinctive feature is the 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 technique of assigning limit points to carefully selected sequences, and Fedorchuk‘s method of resolutions.. . Accessible to readers familiar with the standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers..
出版日期Book 2019
关键词covering dimension; inductive dimension; metric spaces; normal spaces; perfectly normal spaces; Tychonoff
版次1
doihttps://doi.org/10.1007/978-3-030-22232-1
isbn_softcover978-3-030-22234-5
isbn_ebook978-3-030-22232-1Series ISSN 1875-7634 Series E-ISSN 2215-1885
issn_series 1875-7634
copyrightSpringer Nature Switzerland AG 2019
The information of publication is updating

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,-Spaces and the Failure of the Sum and Subset Theorems for ,,,iven ., 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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Antony S. R. Manstead,Gün R. Seminnly defining the meaning of the statement d(.) ≤ . for every non-negative integer . and every space .. It will then be understood that (1) d(.) ≤−1 iff . = ∅, (2) d(.) = . if the statement d(.) ≤ . is false for every integer . ≥−1 and (3) if d(.) ≤ . is true for some integer . ≥−1, then d(.) is the first such integer.
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Wolfgang Stroebe,Klaus Jonas,Miles Hewstoneng a normal subspace .. with .. This shows that the subset theorem for the covering or large inductive dimension of normal Hausdorff spaces does not always hold. The two examples together show that on the class of normal Hausdorff spaces, ., . and . are distinct dimension functions and the only relations between them are . and ..
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Book 2019standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers..
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