{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T14:46:00Z","timestamp":1746801960719,"version":"3.40.5"},"reference-count":18,"publisher":"Wiley","license":[{"start":{"date-parts":[[2007,1,1]],"date-time":"2007-01-01T00:00:00Z","timestamp":1167609600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2007]]},"abstract":"This paper is the second part of a series of papers about a new notion ofT<\/mml:mi><\/mml:math>-homotopy of flows. It is proved that the old definition ofT<\/mml:mi><\/mml:math>-homotopy equivalence does not allow the identification of the directed segment with the 3-dimensional cube. This contradicts a paradigm of dihomotopy theory. A new definition ofT<\/mml:mi><\/mml:math>-homotopy equivalence is proposed, following the intuition of refinement of observation. And it is proved that up to weakS<\/mml:mi><\/mml:math>-homotopy, an oldT<\/mml:mi><\/mml:math>-homotopy equivalence is a newT<\/mml:mi><\/mml:math>-homotopy equivalence. The left properness of the weakS<\/mml:mi><\/mml:math>-homotopy model category of flows is also established in this part. The latter fact is used several times in the next papers of this series.<\/jats:p>","DOI":"10.1155\/2007\/87404","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T02:16:08Z","timestamp":1181182568000},"page":"1-20","source":"Crossref","is-referenced-by-count":0,"title":["T<\/mml:mi><\/mml:math>-Homotopy and Refinement of Observation\u2014Part II: Adding NewT<\/mml:mi><\/mml:math>-Homotopy Equivalences"],"prefix":"10.1155","volume":"2007","author":[{"given":"Philippe","family":"Gaucher","sequence":"first","affiliation":[]}],"member":"311","reference":[{"issue":"2","key":"2","doi-asserted-by":"crossref","first-page":"39","DOI":"10.4310\/HHA.2003.v5.n2.a3","volume":"5","year":"2003","journal-title":"Homology, Homotopy, and Applications"},{"key":"3","first-page":"97","volume":"11","year":"2005","journal-title":"New York Journal of Mathematics"},{"key":"4","first-page":"319","volume":"12","year":"2006","journal-title":"New York Journal of Mathematics"},{"key":"5","first-page":"63","volume":"12","year":"2006","journal-title":"New York Journal of Mathematics"},{"issue":"3","key":"6","first-page":"59","volume":"16","year":"2006","journal-title":"Theory and Applications of Categories"},{"issue":"1","key":"7","doi-asserted-by":"crossref","first-page":"549","DOI":"10.4310\/HHA.2003.v5.n1.a20","volume":"5","year":"2003","journal-title":"Homology, Homotopy, and Applications"},{"key":"8","series-title":"Mathematical Surveys and Monographs","volume-title":"Model Categories","volume":"63","year":"1999"},{"key":"9","series-title":"Mathematical Surveys and Monographs","volume-title":"Model Categories and Their Localizations","volume":"99","year":"2003"},{"volume-title":"Homotopical Algebra","year":"1967","series-title":"Lecture Notes in Mathematics, no. 43","key":"11"},{"volume-title":"Topology: A Geometric Account of General Topology, Homotopy Types and the Fundamental Groupoid","year":"1988","series-title":"Ellis Horwood Series: Mathematics and Its Applications","key":"12"},{"volume-title":"A Concise Course in Algebraic Topology","year":"1999","series-title":"Chicago Lectures in Mathematics","key":"13"},{"issue":"1","key":"15","doi-asserted-by":"crossref","first-page":"51","DOI":"10.4310\/HHA.2005.v7.n1.a4","volume":"7","year":"2005","journal-title":"Homology, Homotopy, and Applications"},{"key":"16","doi-asserted-by":"crossref","first-page":"11","DOI":"10.7146\/math.scand.a-10791","volume":"19","year":"1966","journal-title":"Mathematica Scandinavica"},{"key":"17","doi-asserted-by":"crossref","first-page":"130","DOI":"10.7146\/math.scand.a-10877","volume":"22","year":"1968","journal-title":"Mathematica Scandinavica"},{"key":"18","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1007\/BF01304912","volume":"23","year":"1972","journal-title":"Archiv der Mathematik"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2005.02.006"},{"volume-title":"Notes on Categories and Groupoids","year":"1971","series-title":"Van Nostrand Rienhold Mathematical Studies, no. 32","key":"20"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1007\/s00209-003-0607-y"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2007\/087404.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2007\/087404.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,17]],"date-time":"2017-06-17T14:26:25Z","timestamp":1497709585000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2007\/087404\/abs\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007]]},"references-count":18,"alternative-id":["087404","87404"],"URL":"https:\/\/doi.org\/10.1155\/2007\/87404","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2007]]}}}