MARC Record from marc_columbia

LEADER: 04197cam a22004214a 4500
001 6362240
005 20221122025423.0
008 070530t20082008flua b 001 0 eng
010 $a 2007022732
015 $aGBA771229$2bnb
016 7 $a013834142$2Uk
020 $a9781420060560 (pbk. : alk. paper)
020 $a1420060562 (pbk. : alk. paper)
035 $a(OCoLC)ocn137325272
035 $a(OCoLC)137325272
035 $a(NNC)6362240
035 $a6362240
040 $aDLC$cDLC$dBTCTA$dBAKER$dYDXCP$dUKM$dC#P$dOrLoB-B
050 00 $aQA169$b.O97 2008
082 00 $a512/.62$222
100 1 $aOystaeyen, F. Van,$d1947-$0http://id.loc.gov/authorities/names/n79007748
245 10 $aVirtual topology and functor geometry /$cFred Van Oystaeyen.
260 $aBoca Raton, Fla. :$bChapman & Hall/CRC,$c[2008], ©2008.
300 $axviii, 150 pages :$billustrations ;$c24 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aLecture notes in pure and applied mathematics ;$vv. 256
504 $aIncludes bibliographical references (p. 143-146) and index.
505 00 $g1.$tA Taste of Category Theory -- $g1.1.$tBasic Notions -- $g1.2.$tGrothendieck Categories -- $g1.3.$tSeparable Functors -- $g1.$tNoncommutative Spaces -- $g2.1.$tSmall Categories, Posets, and Noncommutative Topologies -- $g2.2.$tThe Topology of Virtual Opens and Its Commutative Shadow -- $g2.3.$tPoints and the Point Spectrum: Points in a Pointless World -- $g2.4.$tPresheaves and Sheaves over Noncommutative Topologies -- $g2.5.$tNoncommutative Grothendieck Topologies -- $g2.6.$tThe Fundamental Examples I: Torsion Theories -- $g2.7.$tThe Fundamental Examples II: L(H) -- $g2.8.$tOre Sets in Schematic Algebras -- $g3.$tGrothendieck Categorical Representations -- $g3.1.$tSpectral Representations -- $g3.2.$tAffine Elements -- $g3.3.$tQuotient Representations -- $g3.4.$tNoncommutative Projective Space -- $g4.$tSheaves and Dynamical Topology -- $g4.5.$tIntroducing Structure Sheaves -- $g4.4.$tDynamical Presheaves and Temporal Points -- $g4.3.$tThe Spaced-Time Model.
520 1 $a"Intrinsically noncommutative spaces today are considered from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics. From this point of view, it is ideal to devise a concept of space and its geometry that is fundamentally noncommutative. Providing a clear introduction to noncommutative topology, Virtual Topology and Functor Geometry explores new aspects of these areas as well as more established facets of noncommutative algebra." "Presenting the material in an easy, colloquial style to facilitate understanding, the book begins with an introduction to category theory, followed by a chapter on noncommutative spaces. This chapter examines noncommutative lattices, noncommutative opens, sheaf theory, the generalized Stone space, and Grothendieck topology. The author then studies Grothendieck categorical representations to formulate an abstract notion of "affine open". The final chapter proposes a dynamical version of topology and sheaf theory, providing at least one solution of the problem of sheafification independent of generalizations of topos theory." "By presenting new ideas for the development of an intrinsically noncommutative geometry, this book fosters the further unification of different kinds of noncommutative geometry and the expression of observations that involve natural phenomena."--BOOK JACKET.
650 0 $aCategories (Mathematics)$0http://id.loc.gov/authorities/subjects/sh85020992
650 0 $aGrothendieck categories.$0http://id.loc.gov/authorities/subjects/sh85057444
650 0 $aRepresentations of congruence lattices.$0http://id.loc.gov/authorities/subjects/sh85112942
650 0 $aSheaf theory.$0http://id.loc.gov/authorities/subjects/sh85121203
650 0 $aDynamics.$0http://id.loc.gov/authorities/subjects/sh85040316
650 0 $aNoncommutative function spaces.$0http://id.loc.gov/authorities/subjects/sh2003001086
830 0 $aLecture notes in pure and applied mathematics ;$vv. 256.$0http://id.loc.gov/authorities/names/n42037164
852 00 $bmat$hQA169$i.O97 2008