<電子ブック>
Many Valued Topology and its Applications / by Ulrich Höhle
版 | 1st ed. 2001. |
---|---|
出版者 | New York, NY : Springer US : Imprint: Springer |
出版年 | 2001 |
本文言語 | 英語 |
大きさ | VII, 382 p : online resource |
著者標目 | *Höhle, Ulrich author SpringerLink (Online service) |
件 名 | LCSH:Topology LCSH:Mathematical logic FREE:Topology FREE:Mathematical Logic and Foundations |
一般注記 | I Categorical Foundations -- 1 Categorical Preliminaries -- 2 Partially Ordered Monads -- 3 Categorical Basis of Topology -- II Many Valued Topology -- 4 Quantic Basis of Filter Theory -- 5 Many Valued Topological Spaces -- 6 Many Valued Convergence Theory -- III Applications of Many Valued Topology -- 7 Stochastic Metrics -- 8 Stochastic Processes -- 9 Probability Measures -- 10 Topologies on M-Valued Sets -- A.1 Regularity based on ortholattices -- A.2 Topologization of Menger spaces -- Author Index The 20th Century brought the rise of General Topology. It arose from the effort to establish a solid base for Analysis and it is intimately related to the success of set theory. Many Valued Topology and Its Applications seeks to extend the field by taking the monadic axioms of general topology seriously and continuing the theory of topological spaces as topological space objects within an almost completely ordered monad in a given base category C. The richness of this theory is shown by the fundamental fact that the category of topological space objects in a complete and cocomplete (epi, extremal mono)-category C is topological over C in the sense of J. Adamek, H. Herrlich, and G.E. Strecker. Moreover, a careful, categorical study of the most important topological notions and concepts is given - e.g., density, closedness of extremal subobjects, Hausdorff's separation axiom, regularity, and compactness. An interpretation of these structures, not only by the ordinary filter monad, but also by many valued filter monads, underlines the richness of the explained theory and gives rise to new concrete concepts of topological spaces - so-called many valued topological spaces. Hence, many valued topological spaces play a significant role in various fields of mathematics - e.g., in the theory of locales, convergence spaces, stochastic processes, and smooth Borel probability measures. In its first part, the book develops the necessary categorical basis for general topology. In the second part, the previously given categorical concepts are applied to monadic settings determined by many valued filter monads. The third part comprises various applications of many valued topologies to probability theory and statistics as well as to non-classical model theory. These applications illustrate the significance of many valued topology for further research work in these important fields HTTP:URL=https://doi.org/10.1007/978-1-4615-1617-0 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
|
Springer eBooks | 9781461516170 |
|
電子リソース |
|
EB00237923 |
書誌詳細を非表示
データ種別 | 電子ブック |
---|---|
分 類 | LCC:QA611-614.97 DC23:514 |
書誌ID | 4000106337 |
ISBN | 9781461516170 |
類似資料
この資料の利用統計
このページへのアクセス回数:7回
※2017年9月4日以降