000			03577nam a22004935i 4500
001			978-4-431-54397-8
003			DE-He213
005			20140220082927.0
007			cr nn 008mamaa
008			130722s2013 ja | s |||| 0|eng d
020			_a9784431543978 _9978-4-431-54397-8
024	7		_a10.1007/978-4-431-54397-8 _2doi
050		4	_aQA611-614.97
072		7	_aPBP _2bicssc
072		7	_aMAT038000 _2bisacsh
082	0	4	_a514 _223
100	1		_aSakai, Katsuro. _eauthor.
245	1	0	_aGeometric Aspects of General Topology _h[electronic resource] / _cby Katsuro Sakai.
264		1	_aTokyo : _bSpringer Japan : _bImprint: Springer, _c2013.
300			_aXV, 521 p. 79 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringer Monographs in Mathematics, _x1439-7382
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		0	_aMathematics.
650		0	_aFunctional analysis.
650		0	_aGeometry.
650		0	_aDiscrete groups.
650		0	_aTopology.
650	1	4	_aMathematics.
650	2	4	_aTopology.
650	2	4	_aConvex and Discrete Geometry.
650	2	4	_aGeometry.
650	2	4	_aFunctional Analysis.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9784431543961
830		0	_aSpringer Monographs in Mathematics, _x1439-7382
856	4	0	_uhttp://dx.doi.org/10.1007/978-4-431-54397-8
912			_aZDB-2-SMA
999			_c99088 _d99088