Hausdorff gaps and limits
著者
書誌事項
Hausdorff gaps and limits
(Studies in logic and the foundations of mathematics, v. 132)
North-Holland, 1994
大学図書館所蔵 全36件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references and index
内容説明・目次
内容説明
Gaps and limits are two phenomena occuring in the Boolean algebra P( )/fin. Both were discovered by F. Hausdorff in the mid 1930's. This book aims to show how they can be used in solving several kinds of mathematical problems and to convince the reader that they are of interest in themselves. The forcing technique, which is not commonly known, is used widely in the text. A short explanation of the forcing method is given in Chapter 11. Exercises, both easy and more difficult, are given throughout the book.
目次
Notation and terminology. 1. Boolean Algebras. Introduction. Formulas. Atoms. Complete algebras. Homomorphism and filters. Ultrafilters. Extending a homomorphism. Chains and antichains. Problems. 2. Gaps and Limits. Introduction. Dominance. Hausdorff Gaps. The Parovi enko theorem. Types of gaps and limits. Problems. 3. Stone Spaces. The Stone Representation. Subalgebras and homomorphisms. Zero-sets. The Stone- ech compactification. Spaces of uniform ultrafilters. Strongly zero-dimensional spaces. Extremally disconnected spaces. Problems. 4. F-Spaces. Extending a function. Characterization of countable gaps. Construction of Parovi enko spaces. Closed sets in the space . On the Parovi enko theorem. On P-sets in the space . Character of points. Problems. 5. -Base Matrix. Base tree. Stationary sets. -Points. Problems. 6. Inhomogeneity. Kunen's points. A matrix of independent sets. Countable sets in F-spaces. Inhomogeneity of products of compact spaces. Problems. 7. Extending of Continuous Functions. Weak Lindelhoef property. A long convergent sequence. Strongly discrete sets. Problems. 8. The Martin Axiom. Continuous images. The space 1 . On the Parovi enko theorem. Gaps. Homomorphisms of C(X). Problems. 9. Partitions of Antichains. Partition of algebras. Complete algebras. Partition algebras under MA. More on partition algebras. Problems. 10. Small P-Sets in . Proper forcing. On P-filters with the ccc. Problems. 11. Forcing. Set theory and its models. Forcing. Complete embeddings. Cardinal numbers. Selected models. Iterated forcing. The Martin Axiom. Bibliography. Index
「Nielsen BookData」 より