| 000 | 02592nam a22004335i 4500 | ||
|---|---|---|---|
| 001 | 978-3-0348-0006-8 | ||
| 003 | DE-He213 | ||
| 005 | 20140220083738.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 110301s2011 sz | s |||| 0|eng d | ||
| 020 |
_a9783034800068 _9978-3-0348-0006-8 |
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| 024 | 7 |
_a10.1007/978-3-0348-0006-8 _2doi |
|
| 050 | 4 | _aQA299.6-433 | |
| 072 | 7 |
_aPBK _2bicssc |
|
| 072 | 7 |
_aMAT034000 _2bisacsh |
|
| 082 | 0 | 4 |
_a515 _223 |
| 100 | 1 |
_aBukovský, Lev. _eauthor. |
|
| 245 | 1 | 4 |
_aThe Structure of the Real Line _h[electronic resource] / _cby Lev Bukovský. |
| 264 | 1 |
_aBasel : _bSpringer Basel, _c2011. |
|
| 300 |
_aXIV, 542 p. _bonline resource. |
||
| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
||
| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
||
| 490 | 1 |
_aMonografie Matematyczne ; _v71 |
|
| 505 | 0 | _aPreface -- 1 Introduction -- 2 The Real Line -- 3 Topology of Euclidean Spaces -- 4 Measure Theory -- 5 Useful Tools and Technologies -- 6 Descriptive Set Theory -- 7 Decline and Fall of the Duality -- 8 Special Sets of Reals -- 9 Additional Axioms -- 10 Undecidable Statements -- 11 Appendix -- Bibliography -- Index of Notation -- Index. | |
| 520 | _aThe rapid development of set theory in the last fifty years, mainly in obtaining plenty of independence results, strongly influenced an understanding of the structure of the real line. This book is devoted to the study of the real line and its subsets taking into account the recent results of set theory. Whenever possible the presentation is done without the full axiom of choice. Since the book is intended to be self-contained, all necessary results of set theory, topology, measure theory, descriptive set theory are revisited with the purpose to eliminate superfluous use of an axiom of choice. The duality of measure and category is studied in a detailed manner. Several statements pertaining to properties of the real line are shown to be undecidable in set theory. The metamathematics behind it is shortly explained in the appendix. Each section contains a series of exercises with additional results. | ||
| 650 | 0 | _aMathematics. | |
| 650 | 0 | _aGlobal analysis (Mathematics). | |
| 650 | 1 | 4 | _aMathematics. |
| 650 | 2 | 4 | _aAnalysis. |
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer eBooks | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783034800051 |
| 830 | 0 |
_aMonografie Matematyczne ; _v71 |
|
| 856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/978-3-0348-0006-8 |
| 912 | _aZDB-2-SMA | ||
| 999 |
_c106576 _d106576 |
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