MARC Record from harvard_bibliographic_metadata

LEADER: 03579cam a2200409Ia 4500
001 013744363-3
005 20140314185956.0
006 m o d
008 130821s2013 ja a ob 001 0 eng d
020 $z9784431543961
020 $z4431543961
020 $a9784431543978 (electronic bk.)
020 $a443154397X (electronic bk.)
035 0 $aocn856529443
040 $aN$T$cN$T$dYDXCP$dGW5XE$dIDEBK$dNUI$dCOO$dZMC$dHLS
050 4 $aQA611.A34
072 7 $aMAT$x038000$2bisacsh
082 04 $a514$223
100 1 $aSakai, Katsuro.
245 10 $aGeometric aspects of general topology$h[electronic resource] /$cKatsuro Sakai.
260 $aTokyo ;$aNew York :$bSpringer,$cc2013.
300 $a1 online resource (xv, 521 p.)
490 1 $aSpringer monographs in mathematics
505 00 $tPreliminaries --$tMetrization and Paracompact Spaces --$tTopology of Linear Spaces and Convex Sets --$tSimplicial Complexes and Polyhedra --$tDimensions of Spaces --$tRetracts and Extensors --$tCell-Like Maps and Related Topics.
504 $aIncludes bibliographical references and index.
588 $aDescription based on print version record.
520 $aThis 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 cell-like map; and a non-AR metric linear space. The final chapter enables students to understand how deeply related the two theories are. Simplicial complexes are very useful in topology and are indispensable for studying the theories of both dimension and ANRs. There are many textbooks from which some knowledge of these subjects can be obtained, but no textbook discusses non-locally finite simplicial complexes in detail. So, when we encounter them, we have to refer to the original papers. For instance, J.H.C. Whitehead's theorem on small subdivisions is very important, but its proof cannot be found in any textbook. The homotopy type of simplicial complexes is discussed in textbooks on algebraic topology using CW complexes, but geometrical arguments using simplicial complexes are rather easy.
650 7 $aMATHEMATICS / Topology.$2bisacsh
650 0 $aTopology.
650 0 $aDimension theory (Topology)
655 4 $aElectronic books.
776 08 $iPrint version:$tGeometric Aspects of General Topology.$dSpringer Verlag 2013$z9784431543961$w(OCoLC)828891952
830 0 $aSpringer monographs in mathematics.
899 $a415_565982
988 $a20130802
049 $aHLSS
906 $0OCLC