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Titlebook: Geometric Aspects of General Topology; Katsuro Sakai Book 2013 Springer Japan 2013

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發(fā)表于 2025-3-21 17:29:37 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Geometric Aspects of General Topology
編輯Katsuro Sakai
視頻videohttp://file.papertrans.cn/384/383475/383475.mp4
概述The perfect book for acquiring fundamental knowledge of simplicial complexes and the theories of dimension and retracts.Many proofs are illustrated by figures or diagrams for easier understanding.Fasc
叢書名稱Springer Monographs in Mathematics
圖書封面Titlebook: Geometric Aspects of General Topology;  Katsuro Sakai Book 2013 Springer Japan 2013
描述.This book is designed for graduate students to acquire knowledge of dimension theory, ANR theory (theory of retracts), and related topics. These two theories are connected with various fields in geometric topology and in general topology as well. Hence, for students who wish to research subjects in general and geometric topology, understanding these theories will be valuable. Many proofs are illustrated by figures or diagrams, making it easier to understand the ideas of those proofs. Although exercises as such are not included, some results are given with only a sketch of their proofs. Completing the proofs in detail provides good exercise and training for graduate students and will be useful in graduate classes or seminars..Researchers should also find this book very helpful, because it contains many subjects that are not presented in usual textbooks, e.g., dim .X. × .I .= dim .X. + 1 for a metrizable space .X.; the difference between the small and large inductive dimensions; a hereditarily infinite-dimensional space; the ANR-ness of locally contractible countable-dimensional metrizable spaces; an infinite-dimensional space with finite cohomological dimension; a dimension raising
出版日期Book 2013
版次1
doihttps://doi.org/10.1007/978-4-431-54397-8
isbn_softcover978-4-431-54699-3
isbn_ebook978-4-431-54397-8Series ISSN 1439-7382 Series E-ISSN 2196-9922
issn_series 1439-7382
copyrightSpringer Japan 2013
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Geometric Aspects of General Topology978-4-431-54397-8Series ISSN 1439-7382 Series E-ISSN 2196-9922
地板
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https://doi.org/10.1007/978-1-349-17177-4The reader should have finished a first course in Set Theory and General Topology; basic knowledge of Linear Algebra is also a prerequisite. In this chapter, we introduce some terminology and notation. Additionally, we explain the concept of Banach spaces contained in the product of real lines.
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Preliminaries,The reader should have finished a first course in Set Theory and General Topology; basic knowledge of Linear Algebra is also a prerequisite. In this chapter, we introduce some terminology and notation. Additionally, we explain the concept of Banach spaces contained in the product of real lines.
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Dimensions of Spaces,ch . open cover of . has a . open refinement . with .. and then, dim. = . if dim. ≤ . and dim. ≮ .. By ., we mean that . = .. We say that . is .-. if dim. = . and that . is . (.) (dim. < .) if dim. ≤ . for some . ∈ .. Otherwise, . is said to be . (.) (dim. = .). The dimension is a topological invariant (i.e., dim. = dim. if . ≈ . ).
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