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• catalog abstract "Several recent investigations have focused attention on spaces and manifolds which are non-compact but where the problems studied have some kind of "control near infinity". This monograph introduces the category of spaces that are "boundedly controlled" over the (usually non-compact) metric space Z. It sets out to develop the algebraic and geometric tools needed to formulate and to prove boundedly controlled analogues of many of the standard results of algebraic topology and simple homotopy theory. One of the themes of the book is to show that in many cases the proof of a standard result can be easily adapted to prove the boundedly controlled analogue and to provide the details, often omitted in other treatments, of this adaptation. For this reason, the book does not require of the reader an extensive background. In the last chapter it is shown that special cases of the boundedly controlled Whitehead group are strongly related to lower K-theoretic groups, and the boundedly controlled theory is compared to Siebenmann's proper simple homotopy theory when Z = IR or IR2.".
• catalog contributor b2195390.
• catalog contributor b2195391.
• catalog created "c1988.".
• catalog date "1988".
• catalog date "c1988.".
• catalog dateCopyrighted "c1988.".
• catalog description "Bibliography: p. [301]-304.".
• catalog description "Contents: Category Theoretic Foundations -- The Algebraic Topology of Boundedly Controlled Spaces -- The Geometric Boundedly Controlled Whitehead Group -- Free and Projective RPG Modules. The Algebraic Whitehead Groups of RPG -- The Isomorphism between the Geometric and Algebraic Whitehead Groups -- Boundedly Controlled Manifolds and the s-Cobordism Theorem -- Toward Computations -- Bibliography -- Index.".
• catalog description "Several recent investigations have focused attention on spaces and manifolds which are non-compact but where the problems studied have some kind of "control near infinity". This monograph introduces the category of spaces that are "boundedly controlled" over the (usually non-compact) metric space Z. It sets out to develop the algebraic and geometric tools needed to formulate and to prove boundedly controlled analogues of many of the standard results of algebraic topology and simple homotopy theory. One of the themes of the book is to show that in many cases the proof of a standard result can be easily adapted to prove the boundedly controlled analogue and to provide the details, often omitted in other treatments, of this adaptation. For this reason, the book does not require of the reader an extensive background. In the last chapter it is shown that special cases of the boundedly controlled Whitehead group are strongly related to lower K-theoretic groups, and the boundedly controlled theory is compared to Siebenmann's proper simple homotopy theory when Z = IR or IR2.".
• catalog extent "xii, 309 p. ;".
• catalog hasFormat "Boundedly controlled topology.".
• catalog identifier "0387193979 (U.S.)".
• catalog identifier "3540193979".
• catalog isFormatOf "Boundedly controlled topology.".
• catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1323.".
• catalog isPartOf "Lecture notes in mathematics ; 1323".
• catalog issued "1988".
• catalog issued "c1988.".
• catalog language "eng".
• catalog publisher "Berlin ; New York : Springer-Verlag,".
• catalog relation "Boundedly controlled topology.".
• catalog subject "510 s 514/.22 19".
• catalog subject "Algebraic topology.".
• catalog subject "Categories (Mathematics)".
• catalog subject "Complexes.".
• catalog subject "Homotopy theory.".
• catalog subject "Mathematics.".
• catalog subject "Piecewise linear topology.".
• catalog subject "QA3 .L28 no. 1323 QA613.4".
• catalog tableOfContents "Contents: Category Theoretic Foundations -- The Algebraic Topology of Boundedly Controlled Spaces -- The Geometric Boundedly Controlled Whitehead Group -- Free and Projective RPG Modules. The Algebraic Whitehead Groups of RPG -- The Isomorphism between the Geometric and Algebraic Whitehead Groups -- Boundedly Controlled Manifolds and the s-Cobordism Theorem -- Toward Computations -- Bibliography -- Index.".
• catalog title "Boundedly controlled topology : foundations of algebraic topology and simple homotopy theory / Douglas R. Anderson, Hans J. Munkholm.".
• catalog type "text".